69Composing g(x)=f(x+2)-3

The function $\displaystyle f$ is defined by $\displaystyle f(x) = x^2$. The function $\displaystyle g$ is defined by $\displaystyle g(x) = f(x + 2) - 3$. What is the value of $\displaystyle g(1)$? A) −2 B) 1 C) 6 D) 12

g(1) = 6, which is choice C. Plug x=1 into g(x)=f(x+2)−3 to get f(3)−3; since f(x)=x², f(3)=9, so g(1)=9−3=6.