Chapter 2.1, Problem 60AYU

To determine

To find: The domain of the function $f\left( x\right) =\frac{ -x}{ \sqrt{ -x-2 } }$.

Answer to Problem 60AYU

Domain of $f=\left\{x\right|x <-2\}$, or the interval $\left( -\infty ,-2\right)$.

Explanation of Solution

Given:

The function $f\left( x\right) =\frac{ -x}{ \sqrt{ -x-2 } }$

Calculation:

The function $f$ says to divide negative of a number $x$ by the square root of the number $-x-2$. But only nonnegative numbers have real square roots, so the expression under the square root (the radicand) must be nonnegative (greater than or equal to zero). This requires that

$-x-2 >0$

$-x > 2$

$x < -2$

The domain of $f$ is $\{x|x<-2\}$, or the interval $\left( -\infty ,-2\right)$.