# How do you find the range of f(x)=√((x^2)-4)?

Feb 24, 2018

Find the domain first , then go for the range of $f \left(x\right)$

#### Explanation:

$f \left(x\right) = \sqrt{{x}^{2} - 4}$

Domain of $f \left(x\right)$ : ${x}^{2} - 4 \ge 0$

$\Rightarrow \left(x - 2\right) \left(x + 2\right) \ge 0$

rArr D_f : x ∈ (-∞,-2] ∪ [2,∞)

Now,

find the values of $f \left(x\right)$ corresponding to x= -∞,-2,2,∞

$\therefore$ The R_f : f(x) ∈ [0,∞)

This is the graph of the function :-