# Functions - Set of Values

#### elder

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

Find

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

b) The range of f

2.

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

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

#### running-gag

Hi

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

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

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

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

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

Use the same denominator to simplify this expression

elder