# Functions - Set of Values

• July 14th 2010, 07:12 AM
elder
Functions - Set of Values
1. Let $f(x)=\sqrt{(1/x^2)-2)}$

Find

a) The set of real values of x for which f is real and finite

b) The range of f

2.

Let $f(x)=(x+4)/(x+1)$ , x ≠ -1 and $g(x)=(x-2)/(x-4)$ x ≠ 4

Find the set of values of x such that f(x) ≤ g(x)

• July 14th 2010, 07:36 AM
running-gag
Hi

$f(x)=\sqrt{(1/x^2)-2)}$

f is defined when $(1/x^2)-2 \geq 0$

Let $f(x)=(x+4)/(x+1)$ , x ≠ -1 and $g(x)=(x-2)/(x-4)$ x ≠ 4

$g(x) \geq f(x)$

$\displaystyle \frac{x-2}{x-4} - \frac{x+4}{x+1} \geq 0$

Use the same denominator to simplify this expression