Question

In the following exercise, evaluate the function:

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

Function:$f\left(x\right)=-4x+2$

Short answer

a. The value of the function at $x=2$is role="math" $-6.$

b. The value of the function at $x=-1$is $6.$

c. The value of the function at$x=a$is$-4a+2.$

Step-by-step solution

Step 1. Given Information

The given function is$f\left(x\right)=-4x+2.$

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

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

$$\begin{gathered} f\left(2\right)=-4\left(2\right)+2 \\ f\left(2\right)=-8+2 \\ f\left(2\right)=-6 \end{gathered}$$

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

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

$$\begin{gathered} f(-1)=-4(-1)+2 \\ f(-1)=4+2 \\ f(-1)=6 \end{gathered}$$

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

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

$$\begin{gathered} f\left(a\right)=-4\left(a\right)+2 \\ f\left(a\right)=-4a+2 \end{gathered}$$

Step 5. Conclusion

Therefore, we have,

$$\begin{gathered} a.f\left(2\right)=-6 \\ b.f(-1)=6 \\ c.f\left(a\right)=-4a+2 \end{gathered}$$