Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I wasn't sure how to solve for $x$ and create the inverse function given the $\cos(2x)$ term. Whenever I tried to take $\arccos$ there was an $x$ on the other side of the equality which meant I was achieving nothing. How do I proceed with this question?

Edit: I'm still nto entirely following. When I apply the formula I get stuck with the $m(\frac{3\pi}{4})$ term. I have a note which says that by inspection, $m(\frac{3\pi}{4}) = \frac{\pi}{4}$ which I don't follow.

share|cite|improve this question
Use the formula – The Chaz 2.0 Mar 23 '12 at 0:35
@edit: By definition, $m(y) = x$ if and only if $y = h(x)$. So to show that $m(3\pi/4) = \pi/4$, try calculating $h(\pi/4)$... – TMM Mar 23 '12 at 11:40
up vote 5 down vote accepted

You don't need to solve for $x$ (which is a good thing, because it can't be done).

"$m$ is the inverse of $h$" tells you $3m(x)+\cos(2m(x))=x$ (why?). Now differentiate, using the chain rule. You will have to figure out what $m(3\pi/4)$ is, but you should be able to find a number $x$ that makes $h(x)=3\pi/4$.

share|cite|improve this answer
@Patrick, yes, thanks, I'll edit. – Gerry Myerson Mar 23 '12 at 11:03

we have the formula, $(f^{-1})^{\prime}(x)=\frac{1}{f^{\prime}(f^{-1}(x))}$, so we have for that case, $m^{\prime}(\frac{3\pi}{4})=\frac{1}{h^{\prime}(m(\frac{3\pi}{4}))}$

share|cite|improve this answer
That's great, if you're good at remembering formulas. Also, you still have to figure out what $m(3\pi/4)$ is. – Gerry Myerson Mar 23 '12 at 4:55

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.