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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