Math - precalculus - finding domain and inverse functions

Question: Find the domain and the inverse of :

f(x) = log₂ log ₁₀^(x)

I entered this in the calculator and received: Domain = all real numbers except > 1

but I am stuck getting the inverse

do I use f ^-1 (x) ?

can you show me step by step and if my domain is correct.

Thank you!