Step-by-step explanation:
[tex]y = log_{4}( {x}^{4} ) [/tex]
Swap x and y.
[tex]x = log_{4}( {y}^{4} ) [/tex]
Solve for y.
[tex]x= 4 log_{4}(y) [/tex]
[tex] \frac{1}{4} x = log_{4}(y) [/tex]
[tex]4 {}^{ \frac{1}{4}x } = y[/tex]
So the inverse is
[tex]4 {}^{ \frac{x}{4} } = f {}^{ - 1} (x)[/tex]
