Question

Express your answer as a polynomial in standard form.f(x) = 2x2 – x + 12g(x) = -3x – 4Find: (gºf)(x)

Answer 1

Rewrite the expression as follows.

$(g\circ f)(x)=g(f(x))$

Substitute the value of f(x) into the value of x in g(x).

$\begin{gathered} g(f(x))=g(2x^2-x+12) \\ =-3(2x^2-x+12)-4 \end{gathered}$

Simplify the expression by distributing -3 to the trinomial and then combine like terms, -36 and -4.

$\begin{gathered} g(f(x))=-3(2x^2)-3(-x)-3(12)-4 \\ =-6x^2+3x-36-4 \\ =-6x^2+3x-40 \end{gathered}$

Thus, the value of the expression is as follows.

$(g\circ f)(x)=-6x^2+3x-40$