हिंदी

Which One the Following Relations On A = {1, 2, 3} is a Function? F = {(1, 3), (2, 3), (3, 2)}, G = {(1, 2), (1, 3), (3, 1)}

Advertisements
Advertisements

प्रश्न

Which one the following relations on A = {1, 2, 3} is a function?
f = {(1, 3), (2, 3), (3, 2)}, g = {(1, 2), (1, 3), (3, 1)}                                                                                                        [NCERT EXEMPLAR]

Advertisements

उत्तर

As, each element of the domain set has unique image in the relation f = {(1, 3), (2, 3), (3, 2)}
So, f is a function.
Also, the element 1 of the domain set has two images 2 and 3 of the range set in the relation g = {(1, 2), (1, 3), (3, 1)}
So, g is not a function.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Functions - Exercise 2.5 [पृष्ठ ७४]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 2 Functions
Exercise 2.5 | Q 39 | पृष्ठ ७४

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.


Let A = {–1, 0, 1, 2}, B = {–4, –2, 0, 2} and f, g : A → B be functions defined by f(x) = x2 – x, x ∈ A and g(x) = `2|x - 1/2| – 1`, x ∈ A. Are f and g equal?

Justify your answer. (Hint: One may note that two functions f : A → B and g : A → B such that f(a) = g(a) ∀ a ∈ A are called equal functions.)


Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = 5x3 + 4


Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : `f (x) = x/2`


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = x and g(x) = |x| .


Let f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3) (4, 9) (5, 9)}. Show that gof and fog are both defined. Also, find fog and gof.


Let f = {(1, −1), (4, −2), (9, −3), (16, 4)} and g = {(−1, −2), (−2, −4), (−3, −6), (4, 8)}. Show that gof is defined while fog is not defined. Also, find gof.


Let A = {abc}, B = {u vw} and let f and g be two functions from A to B and from B to A, respectively, defined as :
f = {(av), (bu), (cw)}, g = {(ub), (va), (wc)}.
Show that f and g both are bijections and find fog and gof.


 Find fog and gof  if  : f (x) = ex g(x) = loge x .


Find fog and gof  if : f(x) = c, c ∈ R, g(x) = sin `x^2`


Let

f (x) =`{ (1 + x, 0≤ x ≤ 2) , (3 -x , 2 < x ≤ 3):}`

Find fof.


Find f −1 if it exists : f : A → B, where A = {0, −1, −3, 2}; B = {−9, −3, 0, 6} and f(x) = 3 x.


Consider f : R+ → [−5, ∞) given by f(x) = 9x2 + 6x − 5. Show that f is invertible with `f^-1 (x) = (sqrt (x +6)-1)/3 .`


Let A and B be two sets, each with a finite number of elements. Assume that there is an injective map from A to B and that there is an injective map from B to A. Prove that there is a bijection from A to B.


Let C denote the set of all complex numbers. A function f : C → C is defined by f(x) = x3. Write f−1(1).


Let f : R → Rg : R → R be two functions defined by f(x) = x2 + x + 1 and g(x) = 1 − x2. Write fog (−2).


Write the domain of the real function

`f (x) = sqrtx - [x] .`


Write the domain of the real function

`f (x) = 1/(sqrt([x] - x)`.


Write the domain of the real function f defined by f(x) = `sqrt (25 -x^2)`   [NCERT EXEMPLAR]


Let fg : R → R be defined by f(x) = 2x + l and g(x) = x2−2 for all x

∈ R, respectively. Then, find gof.  [NCERT EXEMPLAR]


Let

\[f : R \to R\]  be a function defined by

\[f\left( x \right) = \frac{e^{|x|} - e^{- x}}{e^x + e^{- x}} . \text{Then},\]
 

Let

\[f : R \to R\]
\[f\left( x \right) = \frac{x^2 - 8}{x^2 + 2}\]
Then,  f is


A function f from the set of natural numbers to the set of integers defined by

\[f\left( n \right)\begin{cases}\frac{n - 1}{2}, & \text{when n is odd} \\ - \frac{n}{2}, & \text{when n is even}\end{cases}\]

 


Mark the correct alternative in the following question:

Let f : → R be given by f(x) = tanx. Then, f-1(1) is

 

 


Let D be the domain of the real valued function f defined by f(x) = `sqrt(25 - x^2)`. Then, write D


Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:

h(x) = x|x|


Which of the following functions from Z into Z is bijective?


The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is ____________.


Let f : R → R, g : R → R be two functions such that f(x) = 2x – 3, g(x) = x3 + 5. The function (fog)-1 (x) is equal to ____________.


The function f: R → R defined as f(x) = x3 is:


Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Based on the given information, f is best defined as:


If f: R→R is a function defined by f(x) = `[x - 1]cos((2x - 1)/2)π`, where [ ] denotes the greatest integer function, then f is ______.


Let f(n) = `[1/3 + (3n)/100]n`, where [n] denotes the greatest integer less than or equal to n. Then `sum_(n = 1)^56f(n)` is equal to ______.


The graph of the function y = f(x) is symmetrical about the line x = 2, then ______.


ASSERTION (A): The relation f : {1, 2, 3, 4} `rightarrow` {x, y, z, p} defined by f = {(1, x), (2, y), (3, z)} is a bijective function.

REASON (R): The function f : {1, 2, 3} `rightarrow` {x, y, z, p} such that f = {(1, x), (2, y), (3, z)} is one-one.


Which one of the following graphs is a function of x?

Graph A Graph B

A function is called one-one if different elements of the domain have:


Many students choosing the same favourite subject resembles which type of function?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×