Question

Let f (x) = x2 + 2x -2 and g (x) = 2x + 3. Find (f.g) (-2).

Answer 1

`\begin{gathered} f(x)=x^2+2x-2 \\ g(x)=2x+3 \\ (f\cdot g)(x)=f(x)\cdot g(x)=(x^2+2x-2)(2x+3) \\ (x^2+2x-2)(2x+3)=2x^3+3x^2+4x^2+6x-4x-6 \\ add_{\text{ }}like_{\text{ }}terms\colon \\ (f\cdot g)(x)=2x^3+7x^2+2x-6 \\ (f\cdot g)(-2)=2(-2)^3+7(-2)^2+2(-2)-6 \\ (f\cdot g)(-2)=2(-8)+7(4)-4-6 \\ (f\cdot g)(-2)=-16+28-4-6 \\ (f\cdot g)(-2)=28-26 \\ (f\cdot g)(-2)=2 \end{gathered}`