how are the functions $f(x)=16^{x}$ and $g(x)=16^{\frac{1}{2}x}$ related?\nthe output values of $g(x)$ are…

how are the functions $f(x)=16^{x}$ and $g(x)=16^{\frac{1}{2}x}$ related?\nthe output values of $g(x)$ are one - half the output values of $f(x)$ for the same value of $x$.\nthe output values of $g(x)$ are one - quarter the output values of $f(x)$ for the same value of $x$.\nthe output values of $g(x)$ are the square root of the output values of $f(x)$ for the same value of $x$.\nthe output values of $g(x)$ are the square of the output values of $f(x)$ for the same value of $x$.

how are the functions $f(x)=16^{x}$ and $g(x)=16^{\frac{1}{2}x}$ related?\nthe output values of $g(x)$ are one - half the output values of $f(x)$ for the same value of $x$.\nthe output values of $g(x)$ are one - quarter the output values of $f(x)$ for the same value of $x$.\nthe output values of $g(x)$ are the square root of the output values of $f(x)$ for the same value of $x$.\nthe output values of $g(x)$ are the square of the output values of $f(x)$ for the same value of $x$.

Answer

Explanation:

Step1: Recall exponent - root relationship

We know that $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. For $g(x)=16^{\frac{1}{2}x}=(16^{x})^{\frac{1}{2}}$.

Step2: Compare with $f(x)$

Given $f(x) = 16^{x}$, then $g(x)=\sqrt{f(x)}$. So the output values of $g(x)$ are the square - root of the output values of $f(x)$ for the same value of $x$.

Answer:

The output values of $g(x)$ are the square root of the output values of $f(x)$ for the same value of $x$.