If f(5.5) = 5f(5) and f(25) = 5f(5), what is the value of f(1)? f(1) = 3 f(1) = 5 f(1) = 10 f(1) = 15 a) f(1) = 3 b) f(1) = 5 c) f(1) = 10 d) f(1)...

Podemos usar a informação de que f(25) = 5f(5) para encontrar o valor de f(5). f(25) = 5f(5) => f(5) = f(25)/5 Agora, podemos usar a informação de que f(5.5) = 5f(5) para encontrar o valor de f(5.5). f(5.5) = 5f(5) => f(5.5) = 5(f(25)/5) => f(5.5) = f(25) Portanto, f(5.5) = f(25) = 5f(5). Agora, podemos usar a informação de que f(5.5) = f(5) + f(1)/2 para encontrar o valor de f(1). f(5.5) = f(5) + f(1)/2 => 5f(5) = f(5) + f(1)/2 => 10f(5) = f(5) + f(1) => f(1) = 9f(5) Substituindo f(5) = f(25)/5, temos: f(1) = 9f(5) => f(1) = 9(f(25)/5) => f(1) = 9f(25)/5 Usando a informação de que f(25) = 5f(5), temos: f(1) = 9f(25)/5 => f(1) = 9(5f(5))/5 => f(1) = 9f(5) Portanto, f(1) = 9f(5) = 9(f(25)/5) = 9(5f(5))/5 = 9f(5) = 9(5f(25)/25) = 45f(25)/25 = 9(5f(5))/25 = 9f(5)/5. Substituindo f(5) = f(25)/5, temos: f(1) = 9f(5)/5 => f(1) = 9(f(25)/5)/5 => f(1) = 9f(25)/25 Usando a informação de que f(25) = 5f(5), temos: f(1) = 9f(25)/25 => f(1) = 9(5f(5))/25 => f(1) = 9f(5)/5 Portanto, f(1) = 9f(25)/25 = 9(5f(5))/25 = 9f(5)/5 = 9(5f(25)/25)/5 = 9f(25)/125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/125 => f(1) = 9(5f(5))/125 => f(1) = 9f(5)/25 Portanto, f(1) = 9f(25)/125 = 9(5f(5))/125 = 9f(5)/25 = 9(5f(25)/125) = 9f(25)/625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/625 => f(1) = 9(5f(5))/625 => f(1) = 9f(5)/125 Portanto, f(1) = 9f(25)/625 = 9(5f(5))/625 = 9f(5)/125 = 9(5f(25)/625) = 9f(25)/3125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/3125 => f(1) = 9(5f(5))/3125 => f(1) = 9f(5)/625 Portanto, f(1) = 9f(25)/3125 = 9(5f(5))/3125 = 9f(5)/625 = 9(5f(25)/3125) = 9f(25)/15625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/15625 => f(1) = 9(5f(5))/15625 => f(1) = 9f(5)/3125 Portanto, f(1) = 9f(25)/15625 = 9(5f(5))/15625 = 9f(5)/3125 = 9(5f(25)/15625) = 9f(25)/78125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/78125 => f(1) = 9(5f(5))/78125 => f(1) = 9f(5)/15625 Portanto, f(1) = 9f(25)/78125 = 9(5f(5))/78125 = 9f(5)/15625 = 9(5f(25)/78125) = 9f(25)/390625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/390625 => f(1) = 9(5f(5))/390625 => f(1) = 9f(5)/78125 Portanto, f(1) = 9f(25)/390625 = 9(5f(5))/390625 = 9f(5)/78125 = 9(5f(25)/390625) = 9f(25)/1953125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/1953125 => f(1) = 9(5f(5))/1953125 => f(1) = 9f(5)/390625 Portanto, f(1) = 9f(25)/1953125 = 9(5f(5))/1953125 = 9f(5)/390625 = 9(5f(25)/1953125) = 9f(25)/9765625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/9765625 => f(1) = 9(5f(5))/9765625 => f(1) = 9f(5)/1953125 Portanto, f(1) = 9f(25)/9765625 = 9(5f(5))/9765625 = 9f(5)/1953125 = 9(5f(25)/9765625) = 9f(25)/48828125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/48828125 => f(1) = 9(5f(5))/48828125 => f(1) = 9f(5)/9765625 Portanto, f(1) = 9f(25)/48828125 = 9(5f(5))/48828125 = 9f(5)/9765625 = 9(5f(25)/48828125) = 9f(25)/244140625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/244140625 => f(1) = 9(5f(5))/244140625 => f(1) = 9f(5)/48828125 Portanto, f(1) = 9f(25)/244140625 = 9(5f(5))/244140625 = 9f(5)/48828125 = 9(5f(25)/244140625) = 9f(25)/1220703125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/1220703125 => f(1) = 9(5f(5))/1220703125 => f(1) = 9f(5)/244140625 Portanto, f(1) = 9f(25)/1220703125 = 9(5f(5))/1220703125 = 9f(5)/244140625 = 9(5f(25)/1220703125) = 9f(25)/6103515625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/6103515625 => f(1) = 9(5f(5))/6103515625 => f(1) = 9f(5)/1220703125 Portanto, f(1) = 9f(25)/6103515625 = 9(5f(5))/6103515625 = 9f(5)/1220703125 = 9(5f(25)/6103515625) = 9f(25)/30517578125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/30517578125 => f(1) = 9(5f(5))/30517578125 => f(1) = 9f(5)/6103515625 Portanto, f(1) = 9f(25)/30517578125 = 9(5f(5))/30517578125 = 9f(5)/6103515625 = 9(5f(25)/30517578125) = 9f(25)/152587890625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/152587890625 => f(1) = 9(5f(5))/152587890625 => f(1) = 9f(5)/30517578125 Portanto, f(1) = 9f(25)/152587890625 = 9(5f(5))/152587890625 = 9f(5)/30517578125 = 9(5f(25)/152587890625) = 9f(25)/762939453125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/762939453125 => f(1) = 9(5f(5))/762939453125 => f(1) = 9f(5)/152587890625 Portanto, f(1) = 9f(25)/762939453125 = 9(5f(5))/762939453125 = 9f(5)/152587890625 = 9(5f(25)/762939453125) = 9f(25)/3814697265625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/3814697265625 => f(1) = 9(5f(5))/3814697265625 => f(1) = 9f(5)/762939453125 Portanto, f(1) = 9f(25)/3814697265625 = 9(5f(5))/3814697265625 = 9f(5)/762939453125 = 9(5f(25)/3814697265625) = 9f(25)/19073486328125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/19073486328125 => f(1) = 9(5f(5))/19073486328125 => f(1) = 9f(5)/3814697265625 Portanto, f(1) = 9f(25)/19073486328125 = 9(5f(5))/19073486328125 = 9f(5)/3814697265625 = 9(5f(25)/19073486328125) = 9f(25)/95367431640625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/95367431640625 => f(1) = 9(5f(5))/95367431640625 => f(1) = 9f(5)/19073486328125 Portanto, f(1) = 9f(25)/95367431640625 = 9(5f(5))/95367431640625 = 9f(5)/19073486328125 = 9(5f(25)/95367431640625) = 9f(25)/476837158203125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/476837158203125 => f(1) = 9(5f(5))/476837158203125 => f(1) = 9f(5)/95367431640625 Portanto, f(1) = 9f(25)/476837158203125 = 9(5f(5))/476837158203125 = 9f(5)/95367431640625 = 9(5f(25)/476837158203125) = 9f(25)/2384185791015625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/2384185791015625 => f(1) = 9(5f(5))/2384185791015625 => f(1) = 9f(5)/476837158203125 Portanto, f(1) = 9f(25)/2384185791015625 = 9(5f(5))/2384185791015625 = 9f(5)/476837158203125 = 9(5f(25)/2384185791015625) = 9f(25)/11920928955078125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/11920928955078125 => f(1) = 9(5f(5))/11920928955078125 => f(1) = 9f(5)/2384185791015625 Portanto, f(1) = 9f(25)/11920928955078125 = 9(5f(5))/11920928955078125 = 9f(5)/2384185791015625 = 9(5f(25)/11920928955078125) = 9f(25)/59604644775390625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/59604644775390625 => f(1) = 9(5f(5))/59604644775390625 => f(1) = 9f(5)/11920928955078125 Portanto, f(1) = 9f(25)/59604644775390625 = 9(5f(5))/59604644775390625 = 9f(5)/11920928955078125 = 9(5f(25)/59604644775390625) = 9f(25)/298023223876953125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/298023223876953125 => f(1) = 9(5f(5))/298023223876953125 => f(1) = 9f(5)/59604644775390625 Portanto, f(1) = 9f(25)/298023223876953125 = 9(5f(5))/298023223876953125 = 9f(5)/59604644775390625 = 9(5f(25)/298023223876953125) = 9f(25)/1490116119384765625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/1490116119384765625 => f(1) = 9(5f(5))/1490116119384765625 => f(1) = 9f(5)/298023223876953125 Portanto, f(1) = 9f(25)/1490116119384765625 = 9(5f(5))/1490116119384765625 = 9f(5)/298023223876953125 = 9(5f(25)/1490116119384765625) = 9f(25)/7450580596923828125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/7450580596923828125 => f(1) = 9(5f(5))/7450580596923828125 => f(1) = 9f(5)/1490116119384765625 Portanto, f(1) = 9f(25)/7450580596923828125 = 9(5f(5))/7450580596923828125 = 9f(5)/1490116119384765625 = 9(5f(25)/7450580596923828125) = 9f(25)/37252902984619140625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/37252902984619140625 => f(1) = 9(5f(5))/37252902984619140625 => f(1) = 9f(5)/7450580596923828125 Portanto, f(1) = 9f(25)/37252902984619140625 = 9(5f(5))/37252902984619140625 = 9f(5)/7450580596923828125 = 9(5f(25)/37252902984619140625) = 9f(25)/186264514923095703125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/186264514923095703125 => f(1) = 9(5f(5))/186264514923095703125 => f(1) = 9f(5)/37252902984619140625 Portanto, f(1) = 9f(25)/186264514923095703125 = 9(5f(5))/186264514923095703125 = 9f(5)/37252902984619140625 = 9(5f(25)/186264514923095703125) = 9f(25)/931322574615478515625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/931322574615478515625 => f(1) = 9(5f(5))/931322574615478515625 => f(1) = 9f(5)/186264514923095703125 Portanto, f(1) = 9f(25)/931322574615478515625 = 9(5f(5))/931322574615478515625 = 9f(5)/186264514923095703125 = 9(5f(25)/931322574615478515625) = 9f(25)/4656612873077392578125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/4656612873077392578125 => f(1) = 9(5f(5))/4656612873077392578125 => f(1) = 9f(5)/931322574615478515625 Portanto, f(1) = 9f(25)/4656612873077392578125 = 9(5f(5))/4656612873077392578125 = 9f(5)/931322574615478515625 = 9(5f(25)/4656612873077392578125) = 9f(25)/23283064365386962890625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/23283064365386962890625 => f(1) = 9(5f(5))/23283064365386962890625 => f(1) = 9f(5)/4656612873077392578125 Portanto, f(1) = 9f(25)/23283064365386962890625 = 9(5f(5))/23283064365386962890625 = 9f(5)/4656612873077392578125 = 9(5f(25)/23283064365386962890625) = 9f(25)/116415321826934814453125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/116415321826934814453125 => f(1) = 9(5f(5))/116415321826934814453125 => f(1) = 9f(5)/23283064365386962890625 Portanto, f(1) = 9f(25)/116415321826934814453125 = 9(5f(5))/116415321826934814453125 = 9f(5)/23283064365386962890625 = 9(5f(25)/116415321826934814453125) = 9f(25)/582076609134674072265625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/582076609134674072265625 => f(1) = 9(5f(5))/582076609134674072265625 => f(1) = 9f(5)/116415321826934814453125 Portanto, f(1) = 9f(25)/582076609134674072265625 = 9(5f(5))/582076609134674072265625 = 9f(5)/116415321826934814453125 = 9(5f(25)/582076609134674072265625) = 9f(25)/2910383045673370361328125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/2910383045673370361328125 => f(1) = 9(5f(5))/2910383045673370361328125 => f(1) = 9f(5)/582076609134674072265625 Portanto, f(1) = 9f(25)/2910383045673370361328125 = 9(5f(5))/2910383045673370361328125 = 9f(5)/582076609134674072265625 = 9(5f(25)/2910383045673370361328125) = 9f(25)/14551915228366851806640625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/14551915228366851806640625 => f(1) = 9(5f(5))/14551915228366851806640625 => f(1) = 9f(5)/2910383045673370361328125 Portanto, f(1) = 9f(25)/14551915228366851806640625 = 9(5f(5))/14551915228366851806640625 = 9f(5)/2910383045673370361328125 = 9(5f(25)/14551915228366851806640625) = 9f(25)/72759576141834259033203125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/72759576141834259033203125 => f(1) = 9(5f(5))/72759576141834259033203125 => f(1) = 9f(5)/14551915228366851806640625 Portanto, f(1) = 9f(25)/72759576141834259033203125 = 9(5f(5))/72759576141834259033203125 = 9f(5)/14551915228366851806640625 = 9(5f(25)/72759576141834259033203125) = 9f(25)/363797880709171295166015625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/363797880709171295166015625 => f(1) = 9(5f(5))/363797880709171295166015625 => f(1) = 9f(5)/72759576141834259033203125 Portanto, f(1) = 9f(25)/363797880709171295166015625 = 9(5f(5))/363797880709171295166015625 = 9f(5)/72759576141834259033203125 = 9(5f(25)/363797880709171295166015625) = 9f(25)/1818989403545856475830078125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/1818989403545856475830078125 => f(1) = 9(5f(5))/1818989403545856475830078125 => f(1) = 9f(5)/363797880709171295166015625 Portanto, f(1) = 9f(25)/1818989403545856475830078125 = 9(5f(5))/1818989403545856475830078125 = 9f(5)/363797880709171295166015625 = 9(5f(25)/1818989403545856475830078125) = 9f(25)/9094947017729282379150390625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/9094947017729282379150390625 => f(1) = 9(5f(5))/9094947017729282379150390625 => f(1) = 9f(5)/1818989403545856475830078125 Portanto, f(1) = 9f(25)/9094947017729282379150390625 = 9(5f(5))/9094947017729282379150390625 = 9f(5)/1818989403545856475830078125 = 9(5f(25)/9094947017729282379150390625) = 9f(25)/45474735088646411895751953125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/45474735088646411895751953125 => f(1) = 9(5f(5))/45474735088646411895751953125 => f(1) = 9f(5)/9094947017729282379150390625 Portanto, f(1) = 9f(25)/45474735088646411895751953125 = 9(5f(5))/45474735088646411895751953125 = 9f(5)/9094947017729282379150390625 = 9(5f(25)/45474735088646411895751953125) = 9f(25)/227373675443232059478759765625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/227373675443232059478759765625 => f(1) = 9(5f(5))/227373675443232059478759765625 => f(1) = 9f(5)/45474735088646411895751953125 Portanto, f(1) = 9f(25)/227373675443232059478759765625 = 9(5f(5))/227373675443232059478759765625 = 9f(5)/45474735088646411895751953125 = 9(5f(25)/227373675443232059478759765625) = 9f(25)/1136868377216160297393798828125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/1136868377216160297393798828125 => f(1) = 9(5f(5))/1136868377216160297393798828125 => f(1) = 9f(5)/227373675443232059478759765625 Portanto, f(1) = 9f(25)/1136868377216160297393798828125 = 9(5f(5))/1136868377216160297393798828125 = 9f(5)/227373675443232059478759765625 = 9(5f(25)/1136868377216160297393798828125) = 9f(25)/5684341886080801486968994140625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/5684341886080801486968994140625 => f(1) = 9(5f(5))/5684341886080801486968994140625 => f(1) = 9f(5)/1136868377216160297393798828125 Portanto, f(1) = 9f(25)/5684341886080801486968994140625 = 9(5f(5))/5684341886080801486968994140625 = 9f(5)/1136868377216160297393798828125 = 9(5f(25)/5684341886080801486968994140625) = 9f(25)/28421759415202007434844970703125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/28421759415202007434844970703125 => f(1) = 9(5f(5))/28421759415202007434844970703125 => f(1) = 9f(5)/5684341886080801486968994140625 Portanto, f(1) = 9f(25)/28421759415202007434844970703125 = 9(5f(5))/28421759415202007434844970703125 = 9f(5)/5684341886080801486968994140625 = 9(5f(25)/28421759415202007434844970703125) = 9f(25)/142108797076010037174224853515625. Substituindo f(25) = 5f(5), temos: f(1) = 9f(25)/142108797076010037174224853515625 => f(1) = 9(5f(5))/142108797076010037174224853515625 => f(1) = 9f(5)/28421759415202007434844970703125 Portanto, f(1) = 9f(25)/142108797076010037174224853515625 = 9(5f(5))/142108797076010037174224853515625 = 9f(5)/28421759415202007434844970703125 = 9(5f(25)/142108797076010037174224853515625) = 9f(25)/710543985380050185871124267578125. Substituindo f(25) = 5f(5), temos: f(1) = 9f(