Question

Let h(x)=x^{2}+x+2 and k(x)=2x^{2}+5. Find h(k(x)) . Show each step of your work.

Answer 1

`h\mleft(k(x)\mright)=4x^4+22x^2+32`

Step-by-step explanation:

Given the functions h(x) and k(x) defined as follows:

`\begin{gathered} h\mleft(x\mright)=x^2+x+2 \\ k\mleft(x\mright)=2x^2+5 \end{gathered}`

The composite function h(k(x)) is obtained by replacing x in h(x) with k(x).

`h\mleft(k\mleft(x\mright)\mright)=(2x^2+5)^2+(2x^2+5)+2`

We then simplify to obtain:

`\begin{gathered} =(2x^2+5)(2x^2+5)+2x^2+5+2 \\ =4x^4+10x^2+10x^2+25+2x^2+5+2 \\ =4x^4+22x^2+32 \end{gathered}`