Given the functions:
[tex]\begin{gathered} f\mleft(x\mright)=x^3-3 \\ g\mleft(x\mright)=^3\sqrt[]{x+3} \end{gathered}[/tex]The functions are inverses of each other when:
[tex](f\circ g)(x)=x[/tex]so, we will find (fog)(x) and compare the result with the previous condition
So, We will substitute the function g(x) into the function f(x) instead of (x)
[tex]\begin{gathered} (f\circ g)(x)=(^3\sqrt[]{x+3})^3-3 \\ \end{gathered}[/tex]simplify the function:
[tex]\begin{gathered} (f\circ g)(x)=(x+3)-3 \\ (f\circ g)(x)=x+3-3 \\ \\ (f\circ g)(x)=x \end{gathered}[/tex]So, the final result is the same as the condition
so, the answer will be:
The functions are inverses of each other.
