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

Oct 29, 2015

I found: $y = \arcsin \left[{\log}_{2} \left(f \left(x\right)\right)\right]$

#### Explanation:

I would take the ${\log}_{2}$ on both sides:
${\log}_{2} f \left(x\right) = \cancel{{\log}_{2}} \left({\cancel{2}}^{\sin \left(x\right)}\right)$
and:
${\log}_{2} f \left(x\right) = \sin \left(x\right)$ isolating $x$:
x=arcsin[log_2(f(x)]
So that our inverse function can be written as:
$y = f \left(x\right) = \arcsin \left[{\log}_{2} \left(f \left(x\right)\right)\right]$