Question

If F(x) =8+11 X-3X², finda. What is F (5)? b. What is F (x + b)?c. What is F (-3)?

Answer 1

`\begin{gathered} \text{Given} \\ F(x)=8+11x-3x^2 \end{gathered}`

a. Solve for F(5).

To solve for F(5), substitute x = 5 to the given function, and evaluate accordingly to the operation

`\begin{gathered} F(x)=8+11x-3x^2 \\ F(5)=8+11(5)-3(5)^2 \\ F(5)=8+55-3(25) \\ F(5)=63-75 \\ F(5)=-12 \end{gathered}`

b. Solve for F(x+b)

Again we substitute the paremeters by x+b to the given function, and we get

`\begin{gathered} F(x)=8+11x-3x^2 \\ F(x+b)=8+11(x+b)-3(x+b)^2 \\ F(x+b)=8+11x+11b-3(x^2+2xb+b^2) \\ F(x+b)=8+11x+11b-3x^2-6xb-3b^2 \\ \\ \text{Since we cannot simplify further, we just rearrange} \\ \text{the final answer according to the degree of the terms} \\ F(x+b)=-3x^2-3b^2-6xb+11x+11b+8 \end{gathered}`

c. Solve for F(-3)

Substitute x = -3

`\begin{gathered} F(x)=8+11x-3x^2 \\ F(-3)=8+11(-3)-3(-3)^2 \\ F(-3)=8-33-3(9) \\ F(-3)=-25-27 \\ F(-3)=-52 \end{gathered}`