Find the domain of the function. Write your answer in both set builder and interval notation. `f(x)= (x-2) / sqrt( x + 4)`

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

`f(x)=(x-2)/sqrt(x+4)`

To determine the domain, we need to take note that in fractions zero denominator is not allowed.
Also, in square roots, a negative number inside the square root is not allowed too.

So, set the radicand of the denominator greater than zero, to get the values of x that are allowed
in this function.

`x + 4gt0`

`x+4gt0-4`

`xgt-4`

Hence the domain of the given function in set notation is `{x|xepsiR, xgt-4}.`  And the interval notation of the domain is `(-4,oo)` .

Zaca's profile pic

Zaca | Student, Undergraduate | (Level 1) Salutatorian

Posted on

Domain = all valid x values.

Becuase of the square root and the position of the x in the denominator, we know that x+4 cannot be less than zero and cannot be equal to zero either.

Therefore x+4 must be greater than zero.

`x+4>0`

`x> -4`

` `  Set builder notation:

`{x|x> -4}`

Interval notation:

`(-4, oo)`

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