growth rate calculus question help

Question

stuck on this question. any help appreciated.

Compare the growth rate of the functions f(x) = 4^x and g(x) = 

A. f(x) grows faster than g(x).

B. f(x) and g(x) grow at the same rate.

C. g(x) grows faster than f(x).

D. It cannot be determined.

Answer 1

√(16^x + 2^x) > √16^x√

√16^x = √(4²)^x

√(4²)^x = 4^x

Therefore

√(16^x + 2^x) > 4^x

QED