Function Composition Math Example 4

Solution

1. 1
   $(f \circ g)(x) = f(g(x)) = \sqrt{x^2 + 5}$.
2. 2
   The square root requires $x^2 + 5 \geq 0$. Since $x^2 \geq 0$, we always have $x^2 + 5 \geq 5 > 0$.
3. 3
   The domain is all real numbers: $(-\infty, \infty)$.