To solve the problem of finding the value of [tex]\(x\)[/tex] when [tex]\( g(h(x)) = 4 \)[/tex], we must understand the composition of functions [tex]\(g(x)\)[/tex] and [tex]\(h(x)\)[/tex].
Given:
1. [tex]\( g(x) = 2x \)[/tex]
2. [tex]\( h(x) = x + 1 \)[/tex]
We need to find [tex]\( x \)[/tex] such that [tex]\( g(h(x)) = 4 \)[/tex].
Step-by-step solution:
1. Compute [tex]\( h(x) \)[/tex]:
[tex]\[
h(x) = x + 1
\][/tex]
2. Substitute [tex]\( h(x) \)[/tex] into [tex]\( g(x) \)[/tex] to find [tex]\( g(h(x)) \)[/tex]:
[tex]\[
g(h(x)) = g(x + 1)
\][/tex]
3. Apply the function [tex]\( g \)[/tex] to the expression [tex]\( x + 1 \)[/tex]:
[tex]\[
g(x + 1) = 2(x + 1)
\][/tex]
4. Set this equal to 4, as given by the problem:
[tex]\[
2(x + 1) = 4
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[
2x + 2 = 4
\][/tex]
[tex]\[
2x = 4 - 2
\][/tex]
[tex]\[
2x = 2
\][/tex]
[tex]\[
x = 1
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( g(h(x)) = 4 \)[/tex] is [tex]\( \boxed{1} \)[/tex].
Considering the given answer choices:
- A. 0
- B. 2
- C. 4
- D. 5
None of these choices match the value of [tex]\( x = 1 \)[/tex]. Thus, the correct value is not listed among the provided answer choices.
