Question

Examples 4 and 5 If$f\left(x\right)=-2x-3$ and$g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$f(r+2)$

Short answer

The function value at$x=r+2$ is$-2r-7$

Step-by-step solution

Step 1. Interpreting of function.

$f\left(r+2\right)$Indicates the value of function$f\left(x\right)$ at$x=r+2$

Step 2. Apply substitution method.

Substitute$x=r+2$ into the function$f\left(x\right)$

$f\left(r+2\right)=-2\left(r+2\right)-3$

Step 3. Further calculation:

$\begin{array}{l}f\left(r+2\right)=-2\left(r+2\right)-3\\ f\left(r+2\right)=-2r-4-3\\ f\left(r+2\right)=-2r-7\end{array}$

Thus, the function value at$x=r+2$ is$-2r-7$