The range of the function f(x)
Question:

The range of the function $f(x)=\frac{x+2}{|x+2|}, x \neq-2$ is

(a) {−1, 1}

(b) {−1, 0, 1}

(c) {1}

(d) (0, ∞)

Solution:

(a) {−1, 1}

$f(x)=\frac{x+2}{|x+2|}, x \neq-2$

 

Let $y=\frac{x+2}{|x+2|}$

For $|x+2|>0$,

or $x>-2$,

$y=\frac{x+2}{x+2}=1$

For $|x+2|<0$,

or $x<-2$

$y=\frac{x+2}{-(x+2)}=-1$

Thus, $y=\{-1,1\}$

or range $f(x)=\{-1,1\}$.

 

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