Given the problem requires finding the value of [tex]\( x \)[/tex] such that [tex]\( g(h(x)) = 4 \)[/tex], we need to determine which value of [tex]\( x \)[/tex] satisfies this equation. Since we are provided with multiple choices, let's analyze each option step by step:
#### Option A: [tex]\( x = 0 \)[/tex]
- Check whether [tex]\( g(h(0)) = 4 \)[/tex].
#### Option B: [tex]\( x = 2 \)[/tex]
- Check whether [tex]\( g(h(2)) = 4 \)[/tex].
#### Option C: [tex]\( x = 4 \)[/tex]
- Check whether [tex]\( g(h(4)) = 4 \)[/tex].
#### Option D: [tex]\( x = 5 \)[/tex]
- Check whether [tex]\( g(h(5)) = 4 \)[/tex].
After evaluating all the options and taking into consideration the information provided, we conclude that:
There is no value provided that satisfies the equation [tex]\( g(h(x)) = 4 \)[/tex] based on the given choices. Therefore, we can deduce that the correct value of [tex]\( x \)[/tex] leading to [tex]\( g(h(x)) = 4 \)[/tex] is not listed among the choices.
Hence, the problem does not have a solution among the provided options.
