Question

Can you explain this problem and how do you solve it.

Answer 1

First, we need to find g composed f

`\begin{gathered} (g\circ f)(x)=g(f(x)) \\ g(x)=-7x^2-4x+5 \\ g(f(x))=-7\lbrack f(x)\text{\rbrack}^2-4f(x)+5 \\ g(f(x))=-7(-5x+5)^2-4(-5x+5)+5 \\ g(f(x))=-7\lbrack(-5x)^2+2\cdot(-5x)\cdot5+5^2\rbrack+20x-20+5 \\ g(f(x))=-7(25x^2-50x+25)+20x-15 \\ g(f(x))=-175x^2+350x-175+20x-15 \\ (g\circ f)(x)=-175x^2+370x-190 \end{gathered}`

Now, we need to evaluate the above function when x = 6

`\begin{gathered} (g\circ f)(6)=-175\cdot6^2+370\cdot6-190 \\ (g\circ f)(6)=-6300+2220-190 \\ (g\circ f)(6)=-4270 \end{gathered}`