Inverse trig function

1. Jan 7, 2012

togame

1. The problem statement, all variables and given/known data
My problem is as follows:
find the inverse of
$$3x+1+\sin(x)$$ with the domain $[-\frac{\pi}{2},\frac{\pi}{2}]$

2. Relevant equations

3. The attempt at a solution
for this would I just try to solve as normal by setting y=f(x) then using the fact that $\arcsin(x) = y$ or is this the wrong way of solving this?

2. Jan 8, 2012

Staff: Mentor

You're not going to be able to solve the equation y = f(x) = 3x + 1 + sin(x) for x (to get the inverse x = f-1(y).
What is the exact problem statement? It might be that you are misreading what is being asked for in this problem.

3. Jan 8, 2012

togame

The exact wording for this problem:
$f(x) = 3x + 1 + \sin(x)$ with domain $[-\pi/2, \pi/2]$. Without your calculator, determine the value of $f^{-1}(1)$.

Since this is an inverse function, I was going to try to solve for the inverse function, then solve for $f^{-1}(1)$

4. Jan 8, 2012

SammyS

Staff Emeritus
How is this question related to a problem which requires you to:
Solve $f(x)=1\text{ for }x\,.$​
?

5. Jan 8, 2012

togame

To which question are you referring? I never mentioned having to solve $f(x)=1$

6. Jan 8, 2012

ehild

The problem asks to determine f-1(1)=x. The equation is equivalent to 1 =f(x), that is, 3x+1+sin(x)=1. Solve for x.

ehild

7. Jan 8, 2012

SammyS

Staff Emeritus
I'll state it more clearly.

How are the following two problems related?
Determine the value of $f^{-1}(1)\,.$

Solve $f(x)=1\text{ for }x\,.$​

8. Jan 8, 2012

Staff: Mentor

While that is the general method, if you are lucky the problem is one that can be solved by recognizing it to be a special case that is easy to solve without ploughing all the way through the full general method (even if the general method were possible).

So you are being asked to find the x value (or values) that makes

$3x + 1 + \sin(x) = 1$

Play around with that equation to see whether you can knock it into something that speaks meaningfully to you.

9. Jan 8, 2012

togame

Ah, I see what you guys are talking about now. Thanks for the help. Much appreciated.