English

Redefine the function which is given by f(x) = |x-1|+|1+x|,-2≤x≤2 - Mathematics

Advertisements
Advertisements

Question

Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`

Sum

Solution

f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`

= `{(-x + 1 - 1 - x",", -2 ≤ x < -1),(-x + 1 + x + 1",", -1 ≤ x  < 1),(x - 1 + 1 + x",", 1 ≤ x ≤ 2):}`

= `{{:(-2x",", -2 ≤ x  < - 1),(2",", -1 ≤ x < 1),(2x",", 1 ≤ x ≤ 2):}`

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Relations and Functions - Solved Examples [Page 25]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 2 Relations and Functions
Solved Examples | Q 9 | Page 25

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine

(c) whether f(xy) = f(x) : f(y) holds

 

If f(x) = x2, find \[\frac{f\left( 1 . 1 \right) - f\left( 1 \right)}{\left( 1 . 1 \right) - 1}\]


If f(x) = (x − a)2 (x − b)2, find f(a + b).

 

If \[f\left( x \right) = \frac{x - 1}{x + 1}\] , then show that  

(i) \[f\left( \frac{1}{x} \right) = - f\left( x \right)\]

(ii) \[f\left( - \frac{1}{x} \right) = - \frac{1}{f\left( x \right)}\]


If  \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right) \text{ and}  g\left( x \right) = \frac{3x + x^3}{1 + 3 x^2}\] , then f(g(x)) is equal to

 


The domain of definition of the function  \[f\left( x \right) = \sqrt{x - 1} + \sqrt{3 - x}\] is

 

The domain of the function \[f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}\] is

 

Let  \[f\left( x \right) = \sqrt{x^2 + 1}\ ] . Then, which of the following is correct?

 


If  \[\left[ x \right]^2 - 5\left[ x \right] + 6 = 0\], where [.] denotes the greatest integer function, then 

 


Check if the following relation is function:


Which of the following relations are functions? If it is a function determine its domain and range:

{(0, 0), (1, 1), (1, −1), (4, 2), (4, −2), (9, 3), (9, −3), (16, 4), (16, −4)}


If f(x) = 3x + a and f(1) = 7 find a and f(4).


Check the injectivity and surjectivity of the following function.

f : N → N given by f(x) = x2 


Check the injectivity and surjectivity of the following function.

f : R → R given by f(x) = x3 


Express the following exponential equation in logarithmic form

54° = 1


Express the following logarithmic equation in exponential form

log2 64 = 6


Solve for x.

log2 x + log4 x + log16 x = `21/4`


If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy 


Select the correct answer from given alternatives.

If f(x) =`1/(1 - x)`, then f{f[f(x)]} is


Select the correct answer from given alternatives.

Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is ______.


A function f is defined by f(x) = 2x – 3 find `("f"(0) + "f"(1))/2`


A plane is flying at a speed of 500 km per hour. Express the distance ‘d’ travelled by the plane as function of time t in hour


The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.

Length ‘x’ of
forehand (in cm)
Height 'y' 
(in inches)
35 56
45 65
50 69.5
55 74

Find the length of forehand of a person if the height is 53.3 inches


The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`

 Calculate the value of `"gg" (1/2)`


The range of the function f(x) = `(x - 3)/(5 - x)`, x ≠ 5 is ______.


Find the domain of the following functions given by f(x) = x|x|


Find the range of the following functions given by f(x) = `3/(2 - x^2)`


Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (fg)(x)


Range of the function f(x) = `x/(1 + x^2)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×