Home
Class 12
MATHS
Show that the function f: R(**)to R (**)...

Show that the function `f: R_(**)to R _(**)` defined by `f (x) = 1/x` is one-one and onto, where `R _(**)` is the set of all non-zero numbes. Is the result true, if the domain `R _(**)` is replaced by N with co-domain being same as `R_(**)` ?

Text Solution

Verified by Experts

The correct Answer is:
NO
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.3|14 Videos

  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.4|13 Videos

  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.1|16 Videos

  • PROBABILITY

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos

  • VECTOR ALGEBRA

    NCERT BANGLISH|Exercise Miscellaneous Exercise on chapter 10|19 Videos

Similar Questions

Explore conceptually related problems

Show that the function f: R toR. defined as f (x) =x ^(2), is neither one-one nor onto.

Prove that the function f: R to R, given by f (x) =2x, is one-one and onto.

Show that the function f: R to R given by f (x) = x ^(3) is injective.

Let the function f : R to R be defined by f(x)= 2x + cos x , then f(x)-

Draw the graph of the function f: R to R defined by f(x)=x^(3), x in R .

Let the function f:R to R be defined by f(x)=x+sinx for all x in R. Then f is -

Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f (x) = (x)/(1 + |x|), x in R is one one and onto function.

If the function f: R to R is defined by f(x)=x^(2)-6x-14 , then f^(-1)(2) is equal to -

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

The function f:R to R is defined by f(x)=cos^(2)x+sin^(4)x for x in R . Then the range of f(x) is