The expression [tex]\frac{4}{\sqrt{x+2} }[/tex] is not defined at x= -2 & for all values of x less than -2 .
Step-by-step explanation:
We have , a given expression as [tex]\frac{4}{\sqrt{x+2} }[/tex] : 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, [tex]\frac{4}{\sqrt{x+2} }[/tex] it's a fractional function which means denominator can be 0 . Denominator = [tex]\sqrt{x+2}[/tex] [tex]\neq 0[/tex]
⇒ [tex]\sqrt{x+2}[/tex] [tex]\neq 0[/tex]
⇒ [tex]x+2\neq 0[/tex]
⇒ [tex]x \neq -2[/tex]
So , [tex]x \neq -2[/tex] . Also , Denominator is a square root expression so it can't be negative inside root ∴ [tex]x+2 > 0[/tex] ⇒ [tex]x> -2[/tex] i.e. x must be greater than -2.
Therefore, the expression [tex]\frac{4}{\sqrt{x+2} }[/tex] is not defined at x= -2 & for all values of x less than -2 .
