Home
Class 12
MATHS
Check the injectivity of the following f...

Check the injectivity of the following function f: `R rarr R` is given by f(x) = `x^(3)`

Answer

Step by step text solution for Check the injectivity of the following function f: R rarr R is given by f(x) = x^(3) by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise PART II : Question for Practice Part II ( Long Answer Type Questions) |2 Videos
  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise PART III : Question for Practice Part III ( Very Short Answer Type Questions) |5 Videos
  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise PART II : Question for Practice Part II ( Very Short Answer Type Questions) |6 Videos
  • QUESTION PAPER 2020

    ARIHANT PUBLICATION|Exercise GROUP C (ANSWER ANY ONE QUESTIONS)|13 Videos
  • SAMPLE PAPER 1

    ARIHANT PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS|13 Videos

Similar Questions

Explore conceptually related problems

Check which of the following function is onto and into. (i) f :X rarr Y, given by f(x) = 3x, where X = {0, 1, 2 and Y = {0,3,6). (ii) f: Z rarr Z, given by f(x) = 3x + 2, (Z = set of integers).

Answer any one question (c ) If the function f:R to R is given by f(x) = (x+3)/(3) and g: R to R is given by g(x) = 2x -3 , then find (i) fog (ii) and gof is f^(-1) =g ?

Prove that the greatest integer function f:R rarr R, given by f(x) = [x] is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Let R be the set of all non -zero real numbers. Then show that f: R rarr R given by f(x) = (1)/(x) is one- one and onto.

Find the composition fog and gof and test whether fog = gof when f and g are functions or R given by f(x) = g(x)=(1-x^3)^(1/3)

Write fog if f:R rarr R and g: R rarr R is given by f(x) = | x| and g(x) = |5x - 2|.

Show that the function f: R rarr R given by f(x) = {{:(1,"if" x gt0),(0, "if" x=0),(-1, "if" x lt 0):} is not one - one

State whether the function f : R rarr R, defined by f(x) = 3 - 4x is onto or not.

If f: R rarr R is defined by f(x) = 3x + 2 define f (f (x))

If the function'f : R rarr R is given by f(x) = x^(2) +2 and g:R rarr R is given by g(x) = (x)/(x-1), x ne 1 then find fog and gof and hence find fog (2) and gof (-3) .