To find [tex]\( (f - g)(x) \)[/tex] given the functions [tex]\( f(x) = 8x + 14 \)[/tex] and [tex]\( g(x) = 5x - 2 \)[/tex], follow these steps:
1. Write down the given functions:
[tex]\[
f(x) = 8x + 14
\][/tex]
[tex]\[
g(x) = 5x - 2
\][/tex]
2. Set up the subtraction of the two functions:
[tex]\[
(f - g)(x) = f(x) - g(x)
\][/tex]
3. Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] into the equation:
[tex]\[
(f - g)(x) = (8x + 14) - (5x - 2)
\][/tex]
4. Distribute the negative sign through the [tex]\( g(x) \)[/tex] expression (i.e., apply the subtraction):
[tex]\[
(f - g)(x) = 8x + 14 - 5x + 2
\][/tex]
5. Combine like terms:
- Combine the [tex]\( x \)[/tex]-terms:
[tex]\[
8x - 5x = 3x
\][/tex]
- Combine the constant terms:
[tex]\[
14 + 2 = 16
\][/tex]
6. Finally, write the simplified expression:
[tex]\[
(f - g)(x) = 3x + 16
\][/tex]
So, the function [tex]\( (f - g)(x) \)[/tex] is:
[tex]\[
3x + 16
\][/tex]
