If g(x) is the inverse function of f(x) = x^3+2x+lnx find g'(3),

thanks in advance. If g(x) is the inverse function of f(x) = x^3+2x+lnx find g'(3),

thanks in advance. @Mathematics

Question

If g(x) is the inverse function of f(x) = x^3+2x+lnx find g'(3),

thanks in advance. If g(x) is the inverse function of f(x) = x^3+2x+lnx find g'(3),

thanks in advance. @Mathematics

alfie · Answer

Uhm. I'd say, that such function, is not defined on the whole |R field. So you really cannot find the inverse function. Maybe you could do the restriction with x > 0.

anonymous · Answer

Oh ic, the answer they give me is g'(3) = 1/6

alfie · Answer

Well, if that's the case, let's wait for someone else to double check :).

anonymous · Answer

Sounds good, thanks for your help so far.

anonymous · Answer

By definition, then,
$$g(f(x)) = x$$
So, differentiating both sides,
$$ [g(f(x))]' = g'(f(x))f'(x) = 1$$
by the chain rule.  Therefore,
$$g'(f(x)) = \frac{1}{f'(x)} $$
If you graph the function f(x) (or just guess well) you find that f(1) = 3.  So, we want to find f'(1), which turns out to be 3(1)^2 + 2 + 1 = 6.  Therefore,
$$g'(f(1)) = g'(3) = \frac{1}{f'(3)} = \frac{1}{6} $$

anonymous · Answer

Oh okay, thanks a lot for the help , I appreciate it.