The range of the function f(x)= x+2 |x+2| , x -2 is: - Vidyadip

MCQ

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

✓
$\{-1, 1\}$
B
$\{-1, 0, 1\}$
C
$\{1\}$
D
$(0,\infty)$

✓

Answer

Correct option: A.

$\{-1, 1\}$

$\text{f(x)}=\frac{\text{x}+2}{|\text{x}+2|},\text{ x}\neq-2$
Let $\text{y}=\frac{\text{x}+2}{|\text{x}+2|}$
For $|x + 2| > 0$
Or $x > -2$
$\text{y}=\frac{\text{x}+2}{\text{x}+2}=1$
For $|x + 2| < 0$
Or $x < -2$
$\text{y}=\frac{\text{x}+2}{-(\text{x}+2)}=-1$
Thus, $y = \{-1, 1\}$
Or range $f(x) = \{-1, 1\}$

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