Question

Given the definitions of f(x) and g(x) below, find the value of (gof)(-1). f(x) = 2x2 - x + 1 g(x) = 5x + 15

Answer 1

Let's begin by listing out the information given to us:

$\begin{gathered} f\mleft(x\mright)=2x^2-x+1 \\ g\mleft(x\mright)=5x+15​ \end{gathered}$$\begin{gathered} (g^of)(x)=2(5x+15)^2-x+1 \\ (g^of)(x)=2(5x+15)(5x+15)-x+1 \\ (g^of)(x)=2(25x^2+150x+225)-x+1 \\ (g^of)(x)=50x^2+300x+450-x+1 \\ (g^of)(x)=50x^2+300x-x+450+1 \\ (g^of)(x)=50x^2+299x+451 \\ x=-1 \\ (g^of)(-1)=50(-1^2)+299(-1)+451 \\ (g^of)(-1)=50-299+451 \\ (g^of)(-1)=202 \end{gathered}$