Question

Look at the following expression. Are there any values of x for which the expression is not defined under the set of real numbers? Explain your reasoning. (2 points)
$\frac{4}\sqrt{x+2}$

Answer 1

The expression $\frac{4}{\sqrt{x+2} }$ is not defined at x= -2 & for all values of x  less than -2 .

Step-by-step explanation:

We have , a given expression as $\frac{4}{\sqrt{x+2} }$ : Basically we need to find domain for this function and see for which values of x the above function is undefined . Domain of a function is the set of values of x for which the function is defined . We have a rational expression, $\frac{4}{\sqrt{x+2} }$  it's a fractional function which means denominator can be 0 . Denominator = $\sqrt{x+2}$ $\neq 0$

⇒ $\sqrt{x+2}$ $\neq 0$

⇒ $x+2\neq 0$

⇒ $x \neq -2$

So , $x \neq -2$ . Also , Denominator is a square root expression so it can't be negative inside root ∴ $x+2 > 0$ ⇒ $x> -2$ i.e. x must be greater than -2.

Therefore, the expression $\frac{4}{\sqrt{x+2} }$ is not defined at x= -2 & for all values of x  less than -2 .