2.5 Algebra of Functions

Domains:

• $f(x) = \sqrt{x}$ is defined for $x \ge 0$. $D_f = [0, \infty)$.
• $g(x) = x$ is defined for all $\mathbb{R}$. $D_g = \mathbb{R}$.
• Intersection: $D_f \cap D_g = [0, \infty)$.

$(f+g)(x) = \sqrt{x} + x$. Domain: $[0, \infty)$.

$(fg)(x) = x\sqrt{x} = x^{3/2}$. Domain: $[0, \infty)$.