Home
Class 12
MATHS
If A={1,\ 2,\ 3} , show that an onto ...

If `A={1,\ 2,\ 3}` , show that an onto function `f: A->A` must be one-one

Text Solution

Verified by Experts

Let `f` is not one-one.
Then, at least two elements will have the same image.
If `1` and `2` have same image `1` and `3` has the image `3`,
then `2` has no pre-image.
Hence, `f` is not onto.
But, we are given `f` is an onto function which means our assumption is incorrect.
`:.` f is one-one function.
Promotional Banner

Similar Questions

Explore conceptually related problems

Show that a one-one function f : {1, 2, 3}-> {1, 2, 3} must be onto.

Show that a one-one function f : {1, 2, 3}-> {1, 2, 3} must be onto.

Show that the function f(x)=3x+ 2 is one-one and onto

Show that the function f: R-> R : f(x)=sinx is neither one-one nor onto

If f : ArarrAandA=R-{8/(5)} , show that the function f(x) = (8x+3)/(5x-8) is one -one onto. Hence find f^(-1) .

Show that the modulus function f: R->R , given by f(x)=|x| is neither one-one nor onto.

Let A={-1,\ 0,\ 1} and f={(x ,\ x^2): x in A} . Show that f: A->A is neither one-one nor onto.

Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!=n 1) f is one one into function2) f is one one onto function3) f is many one into funciton4) f is many one onto function then

Let A be a finite set. If f: A->A is an onto function, show that f is one-one also.

Let A be a finite set. If f: AvecA is an onto function, show that f is one-one also.