Home
Class 12
MATHS
The mapping f:ZZ rarr ZZ defined by , f(...

The mapping `f:ZZ rarr ZZ` defined by , `f(x)=3x-2`, for all `x in ZZ`, then f will be ___

A

onto but not one-one

B

one-one but not onto

C

many-one and into

D

many-one and onto

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( very short answer type questions)|22 Videos
  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2 B|6 Videos
  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise Sample questions (Assertion -Reason type C)|3 Videos
  • LOGARITHM

    CHHAYA PUBLICATION|Exercise Long Answer Type Question|12 Videos
  • MATHEMATICAL REASONING

    CHHAYA PUBLICATION|Exercise JEE Main (AIEEE) Archive (2016 )|1 Videos

Similar Questions

Explore conceptually related problems

Discuss the surjectivity of the following mapping: f: ZZ rarr ZZ defined by f(x)=2x-1 , for all x in ZZ , where ZZ is the set of integers.

Let A = {-1,0,1,2,} B= {1,1,2,3,-3} and f: A rarr B be the mapping defined by , f(x)=2x-1 , for all x in A .Then f will be ___

Show that the function f:ZZ rarrZZ defined by f(x)=2x^(2)-3 for all x in ZZ , is not one-one , here ZZ is the set of integers.

Prove that the mapping f: RR rarr RR defined by , f(x)=x^(2)+1 for all x in RR is neither one-one nor onto.

Let ZZ be that set of integers and f:ZZ rarr ZZ be defined by f(x)=2x, for all x in ZZ and g: ZZ rarr ZZ be defined by, (for all x in ZZ) g(x)={((x)/(2) " when x is even" ),(0" when x is odd" ):} Show that, (g o f) =I_(ZZ) , but (f o g) ne I_(ZZ) .

Let NN be the set of natural numbers and D be the set of odd natural numbers. Then show that the mapping f:NN rarr D , defined by f(x)=2x-1, for all x in NN is a surjection.

Let ZZ be the set of integers and the mapping f: ZZ rarr ZZ be defined by, f(x)=x^(2) . State which of the following is equal to f^(-1) (4) ?

Show f:R rarr R defined by f(x)= x^2 + x for all x in R is many one.

If ZZ be the set of integers, prove that the function f: ZZ rarrZZ defined by f(x)=|x| , for all x in Z is a many -one function.

Let the function f: RR rarr RR be defined by, f(x)=x^(3)-6 , for all x in RR . Show that, f is bijective. Also find a formula that defines f ^(-1) (x) .