Question

Suppose that f(x)=x+2x−1 is differentiable and has an inverse for x>1 and f(3)=52. Find (f−1)′(52)Suppose that f(x)=x+2x−1 is differentiable and has an inverse for x>1 and f(3)=52. Find (f−1)′(52)+

Answer 1

Answer:

$(f^{-1})'(x)$ = 1/3

Step-by-step explanation:

$(f^{-1})'(x)$ = $\frac{1}{f'(f^{-1}(x))}$

if f(x) = y, $f^{-1}(y)$ = x, so

$f^{-1}(52)$ = 3 since f(3) = 52

finding f'(3)

f'(x) = 3

f'(3) = 3

$(f^{-1})'(x)$ = 1/f'(x) = 1/3