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:

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

✓

Answer

{-1, 1}

Solution:

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

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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