QuestionFind values of $x$ for which $f(g(x)) = g(f(x))$ where $f(x)=\sqrt{x^{2}-1}$ and $g(x)=\sqrt{x^{2}+1}$.

Studdy Solution
This equation holds true for all real numbers $x$. However, we must consider the domain of the original functions $f(x)$ and $g(x)$. Since $f(x)$ is only defined for $x \geq$ or $x \leq -$, these are the only values of $x$ that make $f(g(x))$ and $g(f(x))$ commutative.
So, the solution is $x \geq$ or $x \leq -$.