Functions

High school review taught in Math 117

Example §

f(x) = $\sqrt{x}$

g(x) = $\sqrt{1-x}$

find f $\pm$ g, fg, $\frac{f}{g}$, $\frac{g}{f}$

Solution:

domain of f is [0, $\infty$)

domain of g is (-$\infty$, 1]

These functions domain intersect at [0, 1]

Function	Formula	Domain
f $\pm$ g	$\sqrt{x}$ $\pm$ $\sqrt{1-x}$	[0, 1]
fg	$\sqrt{x(1-x)}$	[0, 1]
$\frac{f}{g}$	$\sqrt{\frac{x}{1-x}}$	[0, 1)
$\frac{g}{f}$	$\sqrt{\frac{1-x}{x}}$	(0, 1]