Let be $x$ the measure of an angle in degrees and $f(x)$ its measure in radians.

Question

I need help with this exercise:

Let be $x$ the measure of an angle in degrees and $f(x)$ its measure in radians. Find:

1. $f(x)$
2. $f^{-1}(y)$
3. $f(5\pi)$
4. $f^{-1}(900)$

So since $x$ the measure of an angle in degrees and $f(x)$ its measure in radians, then $f(x)=\frac{\pi}{180}x$

Then, $f(x)=y$ that is the measure of the angle in radians, so $f^{-1}(y)$ then is the measure of the angle in degrees. Therefore, $f^{-1}(y)=\frac{180}{\pi}y$

Let me know if my analysis is right please.

Then, I'm confused when it asks $f(5\pi)$ because $5\pi$ is an angle in radians and inside $f$ there is $x$ which is the angle in degrees. So $f(5\pi)$ doesn't make sense to me. If I evaluate with the function $f(x)=\frac{\pi}{180}x$ in $5\pi$ I get $f(5\pi)=\frac{\pi}{180}5\pi=\frac{\pi^{2}}{36}$ which is not making sense to me.

Then $f^{-1}(900)$ is also not making sense to me because in $f^{-1}(y)$, the $y$ is the angle in radians and $900$ to me is in degrees (maybe? because it doesn't have the degree sign).

So if some can help me to clarify this to me I will appreciate it. :)