Question

In the following exercises, evaluate the function:

$$\begin{gathered} a.f\left(2\right) \\ b.f(-1) \\ c.f\left(a\right) \end{gathered}$$

Function:$f\left(x\right)=-6x-3$

Short answer

a. The value of the function at $x=2$is $-15.$

b. The value of the function at $x=-1$is $3.$

c. The value of the function at $x=a$is $-6a-3.$

Step-by-step solution

Step 1. Given Information

The given function is$f\left(x\right)=-6x-3.$

Part (a) Step 1. Evaluating the function at x=2.

To evaluate $f\left(2\right)$, substitute $2$for $x.$

$$\begin{gathered} f\left(2\right)=-6\left(2\right)-3 \\ f\left(2\right)=-12-3 \\ f\left(2\right)=-15 \end{gathered}$$

Therefore,$f\left(2\right)=-15.$

Part (b) Step 2. Evaluating the function at x=-1.

To evaluate $f(-1)$substitute $-1$for $x.$$x.$

$$\begin{gathered} f(-1)=-6(-1)-3 \\ f(-1)=6-3 \\ f(-1)=3 \end{gathered}$$

Therefore,$f(-1)=3.$

Part (c) Step 1. Evaluating the function at x=a.

To evaluate $f\left(a\right)$, substitute $a$for $x.$

$$\begin{gathered} f\left(a\right)=-6\left(a\right)-3 \\ f\left(a\right)=-6a-3 \end{gathered}$$

Therefore,$f\left(a\right)=-6a-3.$