Find g(x) , the inverse of f(x)=log_2(4x)-2

f(x)   = log₂ (4x)  - 2       write f(x)  as y

y =   log₂ (4x)  - 2        add 2 to both sides

y + 2   = log₂(4x)  

This says that, in exponential form :

2^{y + 2}   = 4x           divide both sides by 4

[2^{y + 2} ] / 4   = x       now, exchange x and y

[2^{x + 2} ] / 4  = y       and for y, we can write  f^-1(x)  = g(x)

[2^{x + 2} ] / 4  = g(x)     and this is the inverse