Step 4 To find (f-l)'(x) use the theorem that states that if f is differentiable on an interval I and f has an inverse 1 function g, that is g = f-1, then g is differentiable at any x for which f '(g(x)) ± 0 and g'(x) %3D f'(g(x))' Find the values of f-1(121) and then f'(f-1(121)), f-1(x) = (x + 4)1/3 %3D f-1(121) %3D f'(F-1(121)) = f'I 15 = 31 15 75 75 %3D Step 5 1 Substitute the above values in the expression for (f-1)'(121): f'(F=1(121))" 1 (F-1)'(121) = f'(F=1(121)) 1 75 Thus, (f-1)'(121) = 5

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