Question

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

Answer 1

To solve g(f(x)), we will replace the value of x in g(x) with f(x).

`\begin{gathered} g(x)=x^2-2 \\ g(f(x))=(4x^2+x+1)^2-2 \end{gathered}`

Then, simplify.

a. Apply the exponent.

`\begin{gathered} g(f(x))=(4x^2+x+1)(4x^2+x+1)-2 \\ g(f(x))=16x^4+4x^3+4x^2+4x^3+x^2+x+4x^2+x+1-2_{} \end{gathered}`

b. Arrange the terms starting from the highest degree.

`g(f(x))=16x^4+4x^3+4x^3+4x^2+4x^2+x^2+x+x+1-2`

c. Combine like terms.