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}√(x+2)`

Answer 1

The expression
`(4)/(√(x+2) )` is not defined at x= -2 & for all values of x less than -2 .

Explanation:

We have , a given expression as
`(4)/(√(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,
`(4)/(√(x+2) )` it's a fractional function which means denominator can be 0 . Denominator =
`√(x+2)`
`\\eq 0`

⇒
`√(x+2)`
`\\eq 0`

⇒
`x+2\\eq 0`

⇒
`x \\eq -2`

So ,
`x \\eq -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
`(4)/(√(x+2) )` is not defined at x= -2 & for all values of x less than -2 .