Given:
[tex]\left(x\right)=\left(4x^2-11\right)^3andg\left(x\right)=4x^2-11.[/tex]Required:
Find h(x) if
[tex]f\mleft(x\mright)=h°g\left(x\right)[/tex]Explanation:
[tex]\begin{gathered} f\mleft(x\mright)=h°g\left(x\right) \\ f\mleft(x\mright)=h(g(x)) \end{gathered}[/tex]Let g(x) = x
[tex]f(x)=h(x)[/tex][tex](4x^2-11)^3=x^3[/tex]Solve by taking cube root on both sides.
[tex]x=4x^2-11[/tex][tex]\begin{gathered} g(x)=x \\ g(x)=4x^2-11 \end{gathered}[/tex]