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 ...
$\displaystyle f[g(x)] = x$
$\displaystyle \frac{d}{dx} \left(f[g(x)] = x\right)$
$\displaystyle f'[g(x)] \cdot g'(x) = 1$
$\displaystyle g'(x) = \frac{1}{f'[g(x)]}$