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\(f(x) = {3x-1 \over x-7}\)

a) \(f(-1/2) = {3(-1/2)-1 \over ​(-1/2)-7} = {-3/2-2/2 \over ​-​1/2-14/2} = {-5/2 \over -​​15/2} = 1/3\)

Logo, \([f(-1/2)]^2 = (1/3)^2 = 1/9\)

b)\(f(3x-2) = {3(3x-2)-1 \over (3x-2)-7} = {9x-6-1 \over 3x-9} = {9x-7 \over 3x-9}\)

c) \(f(h) = {3h-1 \over h-7}\) e \(f(0) = {3(0)-1 \over (0)-7} = 1/7\)

\({{f(h) - f(0)} }= {{3h - 1 \over h-7} - {1 \over 7} } = {{21h - 7 - h + 7 \over (h-7)(7)}} = {{20h \over 7h-49}}\)

\({{{f(h) - f(0)} }\over h}= {{{20h \over 7h-49}} \over h} = {20h^2 \over 7h -49}\)

d) \(f(5) = {3(5)-1 \over (5)-7} = {15-1 \over 5-7} = {14 \over -2} = -7\)

Logo \(f(f(5)) = f(-7) = {{3(-7) - 1} \over -7 - 7} = {-22 \over -14} = {11 \over 7}\)