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poizon [28]
2 years ago
9

For which of the following decreasing functions f does (f−1)′(10)=−1/8

Mathematics
1 answer:
Oduvanchick [21]2 years ago
7 0

Recall the inverse function theorem: if f(x) has an inverse, and if f(a) = b and a = f⁻¹(b), then

f⁻¹(f(x)) = x   ⇒   (f⁻¹)'(f(x)) • f'(x) = 1   ⇒   (f⁻¹)'(f(x)) = 1/f'(x)

⇒   (f⁻¹)'(b) = 1/f'(a)

Let b = 10. Then pick the function f(x) such that f(a) = 10 and f'(a) = -8 for some number a.

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