# Thread: Functions - Set of Values

1. ## Functions - Set of Values

1. Let $\displaystyle f(x)=$\sqrt{(1/x^2)-2)}$$Find a) The set of real values of x for which f is real and finite b) The range of f 2. Let \displaystyle f(x)=(x+4)/(x+1) , x ≠ -1 and \displaystyle g(x)=(x-2)/(x-4) x ≠ 4 Find the set of values of x such that f(x) ≤ g(x) Please help. Thanks! 2. Hi \displaystyle f(x)=\sqrt{(1/x^2)-2)}$$

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