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max2010maxim [7]
3 years ago
15

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)+
Mathematics
1 answer:
Lorico [155]3 years ago
6 0

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

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