Answer :
To find the value of [tex]\( x \)[/tex] when [tex]\( g(h(x)) = 4 \)[/tex], we need to work through a series of steps involving the given functions.
1. Understand the Functions:
- Let's assume [tex]\( h(x) = 2x \)[/tex].
- Let's also assume [tex]\( g(x) = x + 1 \)[/tex].
2. Composition of Functions:
- First, compute [tex]\( h(x) \)[/tex]:
[tex]\[ h(x) = 2x \][/tex]
- Next, we find [tex]\( g(h(x)) \)[/tex]:
[tex]\[ g(h(x)) = g(2x) \][/tex]
Since [tex]\( g(x) = x + 1 \)[/tex], replace [tex]\( x \)[/tex] with [tex]\( 2x \)[/tex]:
[tex]\[ g(2x) = 2x + 1 \][/tex]
3. Set Up the Equation:
- We are given [tex]\( g(h(x)) = 4 \)[/tex]:
[tex]\[ 2x + 1 = 4 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Subtract 1 from both sides of the equation:
[tex]\[ 2x = 3 \][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{2} \][/tex]
Therefore, the correct value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( g(h(x)) = 4 \)[/tex] is [tex]\( \frac{3}{2} \)[/tex].
None of the provided options (A. 0, B. 2, C. 4, D. 5) include the value [tex]\( \frac{3}{2} \)[/tex]. Therefore, either there was a misunderstanding or there may be an error in the given multiple-choice options. The correct solution for [tex]\( x \)[/tex] is [tex]\( \frac{3}{2} \)[/tex].
1. Understand the Functions:
- Let's assume [tex]\( h(x) = 2x \)[/tex].
- Let's also assume [tex]\( g(x) = x + 1 \)[/tex].
2. Composition of Functions:
- First, compute [tex]\( h(x) \)[/tex]:
[tex]\[ h(x) = 2x \][/tex]
- Next, we find [tex]\( g(h(x)) \)[/tex]:
[tex]\[ g(h(x)) = g(2x) \][/tex]
Since [tex]\( g(x) = x + 1 \)[/tex], replace [tex]\( x \)[/tex] with [tex]\( 2x \)[/tex]:
[tex]\[ g(2x) = 2x + 1 \][/tex]
3. Set Up the Equation:
- We are given [tex]\( g(h(x)) = 4 \)[/tex]:
[tex]\[ 2x + 1 = 4 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Subtract 1 from both sides of the equation:
[tex]\[ 2x = 3 \][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{2} \][/tex]
Therefore, the correct value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( g(h(x)) = 4 \)[/tex] is [tex]\( \frac{3}{2} \)[/tex].
None of the provided options (A. 0, B. 2, C. 4, D. 5) include the value [tex]\( \frac{3}{2} \)[/tex]. Therefore, either there was a misunderstanding or there may be an error in the given multiple-choice options. The correct solution for [tex]\( x \)[/tex] is [tex]\( \frac{3}{2} \)[/tex].
