Question

4 (02.08 MC)Ler f(x) = 4x+x+ 1 and g(x) = x2- 2. Find a{f(x)). Show each step of your work

Answer 1

Given:

`f(x)=4x^2+x+1\text{ and }g(x)=x^2-2.`

The composition is g(f(x)).

`\text{ Substitute }f\mleft(x\mright)=4x^2+x+1\text{ in the g(f(x)), we get}`
`g(f(x))=g(4x^2+x+1)`
`Replace\text{ }x=4x^2+x+1\text{ in }g(x)=x^2-2,\text{ we get}`

`g(f(x))=(4x^2+x+1)^2-2`
`\text{Use (a+b+c)}^2=a^2+b^2+c^2+2ab+2bc+2ca\text{.}`

`g(f(x))=(4x^2)^2+x^2+1^2+2(4x)(x)+2(4x)(1)+2(x)(1)-2`

`g(f(x))=16x^4+x^2+1+8x^2+8x+2x-2`

Adding like terms, which terms have the same variable with the same power.

`g(f(x))=16x^4+9x^2+10x-1`

Hence the answer is

`g(f(x))=16x^4+9x^2+10x-1`