Question

(8 (2)Step 3 of 4: Find (8. f)(2)Enable Zoom/Pan1018(x) = -x-2510-510$-101f(x) = 2x + 1Answer

Answer 1

We are given the following two functions g(x) and f(x)

`\begin{gathered} g(x)=-x-2 \\ f(x)=2x+1 \end{gathered}`

We are asked to find (g⋅f)(2)

(g⋅f)(x) means to multiply the functions g(x) and f(x)

`\begin{gathered} (g\cdot f)(x)=g(x)\cdot f(x) \\ (g\cdot f)(x)=(-x-2)\cdot(2x+1) \\ (g\cdot f)(x)=-2x^2-x-4x-2 \\ (g\cdot f)(x)=-2x^2-5x-2 \end{gathered}`

Finally, now substitute x = 2 into the function (g⋅f)(x)

`\begin{gathered} (g\cdot f)(2)=-2(2)^2-5(2)-2 \\ (g\cdot f)(2)=-8-10-2 \\ (g\cdot f)(2)=-20 \end{gathered}`

Therefore, (g⋅f)(2) = -20