To find [tex]\( g^{-1}(4) \)[/tex] for the function [tex]\( g(x) = \frac{2x + 2}{4} \)[/tex], we need to find the value of [tex]\( x \)[/tex] that makes [tex]\( g(x) \)[/tex] equal to 4. Here’s the step-by-step process:
1. Set up the equation:
[tex]\[
g(x) = \frac{2x + 2}{4}
\][/tex]
We need to find [tex]\( x \)[/tex] such that [tex]\( g(x) = 4 \)[/tex]. So, we set:
[tex]\[
\frac{2x + 2}{4} = 4
\][/tex]
2. Clear the fraction:
Multiply both sides of the equation by 4 to eliminate the denominator:
[tex]\[
2x + 2 = 16
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Subtract 2 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x = 14
\][/tex]
Divide both sides by 2:
[tex]\[
x = 7
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( g(x) = 4 \)[/tex] is [tex]\( x = 7 \)[/tex].
Therefore, [tex]\( g^{-1}(4) = 7 \)[/tex].
