Question

g of x equals 2 Superscript x Baseline                  h of x equals 3 x
Which expression represents g of left-parenthesis h of left-parenthesis x right-parenthesis right-parenthesis?
Answer options with 4 options
A.
5 Superscript x Baseline
B.
6 Superscript x Baseline
C.
8 Superscript x Baseline
D.
9 Superscript x Baseline

Answer 1

To find \( g(h(x)) \), we need to evaluate the function \( g \) at the output of the function \( h \).

Given:
- \( g(x) = 2^x \)
- \( h(x) = 3x \)

First, find \( h(x) \):
\[
h(x) = 3x
\]

Next, substitute \( h(x) \) into \( g(x) \):
\[
g(h(x)) = g(3x)
\]

Now, using the definition of \( g(x) \):
\[
g(3x) = 2^{3x}
\]

We can simplify \( 2^{3x} \) using the property of exponents:
\[
2^{3x} = (2^3)^x = 8^x
\]

So, we have:
\[
g(h(x)) = 8^x
\]

Thus, the correct answer is:
**C. \( 8^x \)**.