To find the value of [tex]\( a \)[/tex] such that [tex]\( f(a) = a \)[/tex] for the function [tex]\( f(x) = 4x - 2 \)[/tex], follow these steps:
1. Set up the equation:
Given [tex]\( f(a) = a \)[/tex], substitute [tex]\( a \)[/tex] into the function:
[tex]\[
f(a) = 4a - 2
\][/tex]
Therefore, the equation becomes:
[tex]\[
4a - 2 = a
\][/tex]
2. Rearrange the equation:
To isolate [tex]\( a \)[/tex], first move all terms involving [tex]\( a \)[/tex] to one side of the equation. Subtract [tex]\( a \)[/tex] from both sides:
[tex]\[
4a - 2 - a = 0
\][/tex]
Simplify the left side:
[tex]\[
3a - 2 = 0
\][/tex]
3. Solve for [tex]\( a \)[/tex]:
Next, isolate [tex]\( a \)[/tex] by first adding 2 to both sides:
[tex]\[
3a - 2 + 2 = 2
\][/tex]
Simplifying, we get:
[tex]\[
3a = 2
\][/tex]
Now, divide both sides by 3 to solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{2}{3}
\][/tex]
Thus, the value of [tex]\( a \)[/tex] that satisfies [tex]\( f(a) = a \)[/tex] for the function [tex]\( f(x) = 4x - 2 \)[/tex] is:
[tex]\[
a = \frac{2}{3}
\][/tex]
