(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume the function f defined by f(x)=5x+sin(πx) is strictly increasing on ℝ. Find (f[itex]^{-1}[/itex])'(10)

2. Relevant equations

Let I and J be be intervals and let f:I->J be a continuous, strictly monotone function. If f is differentiable at c and if f'(c)≠0, then (f[itex]^{-1}[/itex]) is differentiable at f(c) and (f[itex]^{-1}[/itex])'(f(c))= 1/f'(c)

3. The attempt at a solution

It is clear f is continuous and differentiable on ℝ.

=> f'(x) = 5+πcos(πx)

Finding when f(x)=10,

10 = 5x+sin(πx) => x=2

Then (f[itex]^{-1}[/itex])'(f(2))=1/f'(2) = 1/(5+πcos(2π)) = 1/(5+(π))

Is this how to do it, or do I use f(10) instead of finding when f(x) is 10?

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