# What is the domain and range of g(x)=-sqrt(x^2-4)?

Feb 27, 2017

Domain: $\left(- \infty , - 2\right] , \left[2 , \infty\right)$
Range: $\left(- \infty , 0\right]$

#### Explanation:

The domain is limited by the square root:

${x}^{2} - 4 \ge 0$
${x}^{2} \ge 4$
$x \le - 2 \mathmr{and} x \ge 2$

The range limit comes from the domain:
When $x = - 2 \mathmr{and} x = 2 , g \left(x\right) = 0$
When $x < - 2 \mathmr{and} x > 2 , g \left(x\right) < 0$

So:
Domain: $\left(- \infty , - 2\right] , \left[2 , \infty\right)$
Range: $\left(- \infty , 0\right]$