Question

1. for the function ( f(x) = 8x - 3 ), find each of the following.

a. ( f(-9) )

b. ( f(x) = 5 )

c. ( f(x) = -x + 15 )

Explanation:

Part a: Find \( f(-9) \)

Step 1: Substitute \( x = -9 \) into \( f(x) \)

Given \( f(x) = 8x - 3 \), substitute \( x=-9 \):
\( f(-9)=8(-9)-3 \)

Step 2: Calculate the value

First, calculate \( 8(-9) = -72 \). Then subtract 3:
\( f(-9)=-72 - 3=-75 \)

Part b: Find \( f(5) \) (assuming the question is \( f(5) \) as per the work shown)

Step 1: Substitute \( x = 5 \) into \( f(x) \)

Given \( f(x) = 8x - 3 \), substitute \( x = 5 \):
\( f(5)=8(5)-3 \)

Step 2: Calculate the value

First, calculate \( 8(5)=40 \). Then subtract 3:
\( f(5)=40 - 3 = 37 \)

Part c: Solve \( f(x)=-x + 15 \) for \( x \) (assuming the question is to solve \( 8x - 3=-x + 15 \))

Step 1: Add \( x \) to both sides

\( 8x - 3+x=-x + 15+x \)
Simplify: \( 9x - 3=15 \)

Step 2: Add 3 to both sides

\( 9x - 3+3=15 + 3 \)
Simplify: \( 9x=18 \)

Step 3: Divide by 9

\( x=\frac{18}{9}=2 \)

Answer:

s:
a. \( \boldsymbol{f(-9)=-75} \)
b. \( \boldsymbol{f(5)=37} \) (if the input is \( x = 5 \))
c. \( \boldsymbol{x = 2} \) (if solving \( f(x)=-x + 15 \))