# domain of function

• Jan 21st 2010, 12:43 PM
bastropgarl
domain of function
Im not quite sure how to find the domain on the function f(x)=the square root of x squared-4
• Jan 21st 2010, 12:47 PM
e^(i*pi)
Quote:

Originally Posted by bastropgarl
Im not quite sure how to find the domain on the function f(x)=the square root of x squared-4

$\displaystyle f(x) \geq 0$ therefore $\displaystyle \sqrt{x^2-4} = \sqrt{(x-2)(x+2)} \geq 0$

Solve for x.
• Jan 21st 2010, 12:57 PM
masters
Quote:

Originally Posted by bastropgarl
Im not quite sure how to find the domain on the function f(x)=the square root of x squared-4

Hi bastropgarl,

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

The domain is all values of x such that $\displaystyle x^2-4 \ge 0$

This graph has x-intercepts are -2 and +2.

The domain will be the values to the left of -2 and to the right of +2. The values between -2 and +2 are not part of the domain. For instance, zero is not in the domain.

Domain = $\displaystyle \{x|x \ge 2 \ \ or \ \ x \le -2\}$