If X={1,2,3,4}, then one-one onto mappin...

If `X={1,2,3,4},` then one-one onto mappings `f:X to X` such that `f(1)=1, f(2) ne 2 f(4) ne 4` are given by

A

{(1,1),(2,3),(3,4),(4,2)}

B

{(1,1),(2,4),(3,3),(4,2)}

C

{(1,1),(2,4),(3,2),(4,3)}

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

A,B,C

Clearly, mappings given in options (a),(b) and (c ) satisfy the given conditions and are one-one onto.

Topper's Solved these Questions

FUNCTIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|49 Videos
FUNCTIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|10 Videos
DISCRETE PROBABILITY DISTRIBUTIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos
HYPERBOLA
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

Let f: R → R be a one-one onto differentiable function, such that f(2)=1 and f^(prime)(2)=3. Then, find the value of (d/(dx)(f^(-1)(x)))_(x=1)

Let f: RvecR be a one-one onto differentiable function, such that f(2)=1a n df^(prime)(2)=3. The find the value of ((d/(dx)(f^(-1)(x))))_(x=1)

Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be

Let f(x) =ax^(2) + bx + c and f(-1) lt 1, f(1) gt -1, f(3) lt -4 and a ne 0 , then

Show that if f_1a n df_2 are one-one maps from RtoR , then the product f_1×f_2: RtoR defined by (f_1×f_2)(x)=f_1(x)f_2(x) need not be one-one.

If A = {1, 2, 3, 4} and B= {1, 2, 3, 4, 5, 6} are two sets and function F: A to B is defined by f(x) = x+2, AA x in A , then prove that the function is one-one and into.

For real x, let f(x)""=""x^3+""5x""+""1 , then (1) f is oneone but not onto R (2) f is onto R but not oneone (3) f is oneone and onto R (4) f is neither oneone nor onto R

If R is the set of real numbers then prove that a function f: R to R defined as f(x)=(1)/(x), x ne 0, x in R, is one-one onto.

A function f: R to R is defined as f(x)=4x-1, x in R, then prove that f is one - one.

OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Chapter Test

If X={1,2,3,4}, then one-one onto mappings f:X to X such that f(1)=1, ...
Text Solution
|
The number of bijective functions from set A to itself when A contains...
Text Solution
|
If f(x)=|sin x| then domain of f for the existence of inverse of
Text Solution
|
The function f:[-1//2,\ 1//2]->[-pi//2,pi//2\ ] defined by f(x)=s in^(...
Text Solution
|
Let f: R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(-x)...
Text Solution
|
If f: (e,oo) rarr R & f(x)=log[log (logx)], then f is - (a)f is one-...
Text Solution
|
Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) , where m!=n...
Text Solution
|
Find the inverse of the function: f(x)=(e^(x)-e^(-x))/(e^(x)+e^(-x))+2
Text Solution
|
Find the inverse of the function :y=(1 0^x-1 0^(-x))/(1 0^x+1 0^(-x))+...
Text Solution
|
Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)),(x ne 0) then f(x) equals
Text Solution
|
Let f : R rarr R, g : R rarr R be two functions given by f(x) = 2x - 3...
Text Solution
|
If g(x)=1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) is equal to
Text Solution
|
If f(x)=(1-x)/(1+x), x ne 0, -1 and alpha=f(f(x))+f(f((1)/(x))), then
Text Solution
|
Let f:R to R be a function defined by f(x)=(x^(2)-8)/(x^(2)+2). Then f...
Text Solution
|
If f:(-oo,2]to (-oo,4] where f(x), then f ^(-1) (x) is given by :
Text Solution
|
Find the inverse of the function, (assuming onto). " " ...
Text Solution
|
f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :
Text Solution
|
If f(x)=log((1+x)/(1-x))a n dt h e nf((2x)/(1+x^2)) is equal to {f(x)...
Text Solution
|
If f(x)=(2^x+2^(-x))/2 , then f(x+y)f(x-y) is equals to 1/2{f(2x)+f(2y...
Text Solution
|
The function f:R to R given by f(x)=x^(2)+x is
Text Solution
|
Let f:R to R and g:R to R be given by f(x)=3x^(2)+2 and g(x)=3x-1 for ...
Text Solution
|