Question

If f(x) =(4x^2 -11)^3 and g(x) = 4x^2 -11. given that f(x) = (h°g)(x) find h(x)

Answer 1

Given:

`\left(x\right)=\left(4x^2-11\right)^3andg\left(x\right)=4x^2-11.`

Required:

Find h(x) if

`f\mleft(x\mright)=h°g\left(x\right)`

Step-by-step explanation:

`\begin{gathered} f\mleft(x\mright)=h°g\left(x\right) \\ f\mleft(x\mright)=h(g(x)) \end{gathered}`

Let g(x) = x

`f(x)=h(x)`
`(4x^2-11)^3=x^3`

Solve by taking cube root on both sides.

`x=4x^2-11`
`\begin{gathered} g(x)=x \\ g(x)=4x^2-11 \end{gathered}`