# Thread: solve for f -1

1. ## solve for f -1

hey guys
i had a problem and i just need someone to check if the answer is right

Find the value of d f -1/dx at x =f(a)

f(x) = 4x + 9, a = -2

i got 1/4 for the answer, is that right?

2. ## Re: solve for f -1

Originally Posted by ubhutto
hey guys
i had a problem and i just need someone to check if the answer is right

Find the value of d f -1/dx at x =f(a)

f(x) = 4x + 9, a = -2

i got 1/4 for the answer, is that right?
since the inverse of f(x) is a linear function with slope = 1/4, your solution is correct.

for the general case, if f(x) and g(x) are inverse functions, then ...

$f[g(x)] = x$

$\frac{d}{dx} \left(f[g(x)] = x\right)$

$f'[g(x)] \cdot g'(x) = 1$

$g'(x) = \frac{1}{f'[g(x)]}$

thanks alot
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