Question

Evaluate the function f(x) =4x +1 at the given values of the independent variable and simplify.

a. f(-9)

b. f(x+5)

c. f(-x)

a. f(-9)= (Simplify your answer.)

b. f(x+5)= (Simplify your answer.)

c. f(-x)= (Simplify your answer.)

Answer 1

To evaluate the function \( f(x) = 4x + 1 \) at the given values, let's solve each:

### a. \( f(-9) \)

To find \( f(-9) \), substitute \(-9\) for \(x\):

\[
f(-9) = 4(-9) + 1
\]
\[
= -36 + 1
\]
\[
= -35
\]

So,
\[
\text{a. } f(-9) = -35
\]

### b. \( f(x+5) \)

To find \( f(x+5) \), substitute \(x + 5\) for \(x\):

\[
f(x+5) = 4(x+5) + 1
\]
\[
= 4x + 20 + 1
\]
\[
= 4x + 21
\]

So,
\[
\text{b. } f(x+5) = 4x + 21
\]

### c. \( f(-x) \)

To find \( f(-x) \), substitute \(-x\) for \(x\):

\[
f(-x) = 4(-x) + 1
\]
\[
= -4x + 1
\]

So,
\[
\text{c. } f(-x) = -4x + 1
\]

### Summary of Results:
- **a.** \( f(-9) = -35 \)
- **b.** \( f(x+5) = 4x + 21 \)
- **c.** \( f(-x) = -4x + 1 \)