Question

If the function f(x) = x³ + e^x/2 and g(x) = f^-1(x), then the value of g′(1) is _____.

Answer 1

f(0) = 1, f'(x) = 3x² + 1/2e^x/2

⇒ f'[g(x)]g'(x) = 1

Put x = 0, we get

g'(1) = 1/f'(0) = 2.