Answer:
c. g(x) = h(x)
Step-by-step explanation:
Given functions:
[tex]f(x) = 3^x+11[/tex]
[tex]g(x)=2^{3x+5}[/tex]
[tex]h(x)=32(8^x)[/tex]
Rewrite function g(x) using exponent rules.
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies g(x)=2^{3x} \cdot 2^5[/tex]
[tex]\implies g(x)=2^{3x} \cdot 32[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies g(x)=(2^3)^{x} \cdot 32[/tex]
[tex]\implies g(x)=8^{x} \cdot 32[/tex]
[tex]\implies g(x)=32(8^{x})[/tex]
Therefore, g(x) = h(x).
