To solve for [tex]\( m \)[/tex] given that [tex]\( f(x) = 2x + 2 \)[/tex] and [tex]\( f(m) = 14 \)[/tex], follow these steps:
1. Start with the function [tex]\( f(x) = 2x + 2 \)[/tex].
2. Substitute [tex]\( m \)[/tex] into the function which gives us [tex]\( f(m) = 2m + 2 \)[/tex].
3. We are given that [tex]\( f(m) = 14 \)[/tex]. Therefore, we can set up the equation:
[tex]\[
2m + 2 = 14
\][/tex]
4. To solve for [tex]\( m \)[/tex], we first isolate [tex]\( 2m \)[/tex] by subtracting 2 from both sides of the equation:
[tex]\[
2m + 2 - 2 = 14 - 2
\][/tex]
Simplifying, we get:
[tex]\[
2m = 12
\][/tex]
5. Next, divide both sides of the equation by 2 to solve for [tex]\( m \)[/tex]:
[tex]\[
m = \frac{12}{2}
\][/tex]
6. Simplifying the division, we find:
[tex]\[
m = 6
\][/tex]
So, the value of [tex]\( m \)[/tex] is [tex]\( 6 \)[/tex].
