Given function $$f:y=2-\arccos (4x+3)$$ find the inverse function and the domain of the inverse function.
For the inverse function I got: $$\bar{f}: y=\frac{\cos(2-x)-3}{4} $$
Now the domain of $f$ is $\left [ -1, -\frac{1}{2} \right ]$.
What's the domain of $\bar{f}$? All real numbers? I'm somewhat doubtful whether I got the inverse function right.
Update:
The domain of $arccos(x)$ is $\left [0, \pi\right ]$. Then if we multiply it by $-1$ and add $+2$ we get the range of $f$ is $\left [ 2- \pi, 2 \right ]$ and that's also the domain of $\bar{f}$. Correct?