Question

given the function $f(x)=\frac{1}{2}\sqrt{x}$, use $f(g(x))$ to verify or disprove the proposed inverse function $g(x)=4x^2$.
the function g(x) is not the inverse of f(x) because f(g(x)) select equal x.
select
does not
does

Explanation:

Step1: Substitute g(x) into f(x)

$f(g(x)) = \frac{1}{2}\sqrt{4x^2}$

Step2: Simplify the square root term

$\sqrt{4x^2} = 2|x|$, so $f(g(x)) = \frac{1}{2} \cdot 2|x| = |x|$

Step3: Compare to x

$|x|
eq x$ for negative x

Answer:

The function g(x) is not the inverse of f(x) because f(g(x)) does not equal x.