Answered

Find [tex]g^{-1}(4)[/tex] if [tex]g(x)=\frac{2x+2}{4}[/tex].

Type your numerical answer below.



Answer :

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].