Question

NO LINKS!!

Use the properties of exponents to determine which functions (if any) are the same.
f(x)= 3^x + 11
g(x) = 2^(3x+5)
h(x)= 32(8^x)
a. f(x) = g(x)
b. f(x) = h(x)
c. g(x)=h(x)
d. All three functions are equal
e. None of the functions are equal

Answer 1

c. g(x) = h(x)

Explanation:

Given functions:

`f(x) = 3^x+11`

`g(x)=2^(3x+5)`

`h(x)=32(8^x)`

Rewrite function g(x) using exponent rules.

`\textsf{Apply exponent rule} \quad a^(b+c)=a^b \cdot a^c:`

`\implies g(x)=2^(3x) \cdot 2^5`

`\implies g(x)=2^(3x) \cdot 32`

`\textsf{Apply exponent rule} \quad a^(bc)=(a^b)^c:`

`\implies g(x)=(2^3)^(x) \cdot 32`

`\implies g(x)=8^(x) \cdot 32`

`\implies g(x)=32(8^(x))`

Therefore, g(x) = h(x).