Question

What is the inverse of `f(x) = 2^sin(x)` ?

Answer 1

I found: `y=arcsin[log_2(f(x))]`

Explanation:

I would take the `log_2` on both sides:
`log_2f(x)=cancel(log_2)(cancel(2)^(sin(x)))`
and:
`log_2f(x)=sin(x)` isolating `x`:
`x=arcsin[log_2(f(x)]`
So that our inverse function can be written as:
`y=f(x)=arcsin[log_2(f(x))]`