Solve the problem.
-Let $g ( x ) = \sqrt { x }$. Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = | x |$.
A) $f ( x ) = x ^ { 2 }$
B) $f ( x ) = \frac { 1 } { x ^ { 2 } }$
C) $f ( x ) = x$
D) $f ( x ) = \frac { 1 } { x }$

Question

Quizplus · Accepted Answer

The composition $f \circ g$ means applying $g$ first and then $f$. Given $g(x) = \sqrt{x}$, applying $f$ should result in $|x|$. Squaring a square root, as in $f(x) = x^2$, undoes the square root and handles both positive and negative $x$ values, matching the absolute value function.

Solve the Problem g(x)=xg ( x ) = \sqrt { x }g(x)=x​

Solve the Problem $g ( x ) = \sqrt { x }$