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}

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Functions→Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Let $a, b$ be non-zero real numbers. Which of the following statements about the quadratic equation $a x^2+(a+b) x+b=0$ is necessarily true?

$I$. It has at least one negative root.

$II$. It has at least one positive root.

$III$. Both its roots are real.

Find the derivative of $ e^{x^2} $:

A bag contains $5$ white, $7$ black and $4$ red balls. Three balls are drawn from the bag at random. The probability that all the three balls are white, is

Let in a series of $2 n$ observations, half of them are equal to $a$ and remaining half are equal to $-a.$ Also by adding a constant $b$ in each of these observations, the mean and standard deviation of new set become $5$ and $20 ,$ respectively. Then the value of $a^{2}+b^{2}$ is equal to ....... .

Let the digits $a, b, c$ be in $A.P.$ Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in $A.P.$ at least once. How many such numbers can be formed?

The most frequently occurring data value in a data set is the $...........$

The value of ${(1 + i)^8} + {(1 - i)^8}$ is

If the equation of the locus of a point equidistant from the points $({a_1},{b_1})$ and $({a_2},{b_2})$ is $({a_1} - {a_2})x + ({b_1} - {b_2})y + c = 0$, then the value of $‘c’$ is

If $K = sin^6x + cos^6x$, then $K$ belongs to the interval

The negation of the statement. “A circle is an ellipse” is.