Let $f(x) = |x|$ and $g(x) = x^2$.

Question

Find all values of $x$ for which $f(x) = g(x)$

Answer 1

Since $f(x) = |x|$ is defined piecewise, we need to consider two cases: $x \geq 0$ and $x < 0$.

Case 1: $x \geq 0$
In this case, $f(x) = |x| = x$ and $g(x) = x^2$. So, we need to solve the equation $x = x^2$, which gives $x=0$ or $x=1$.

Case 2: $x < 0$
In this case, $f(x) = |x| = -x$ and $g(x) = x^2$. So, we need to solve the equation $-x = x^2$, which gives $x=-1$.

Therefore, the solution set is $\{-1, 0, 1\}$.