Home
Class 12
MATHS
Show that the function f : R to R, defin...

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 real numbers.

Text Solution

Verified by Experts

The correct Answer is:
f is both one-one and onto.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise THREE MARKS QUESTIONS WITH ANSWERS|16 Videos

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise SIX MARKS QUESTIONS WITH ANSWERS|7 Videos

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise TRY YOURSELF - EXERCISE (Five marks questions)|1 Videos

  • PUC SUPPLEMENTARY EXAMINATION QUESTION PAPER JUNE 2019

    SUBHASH PUBLICATION|Exercise PART E|4 Videos

  • SUPER MODEL QUESTION PAPER FOR PRACTICE

    SUBHASH PUBLICATION|Exercise PART - E|4 Videos

Similar Questions

Explore conceptually related problems

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_(**) ?

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

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

Show that the function f: N to N given by f(x)=2x is one-one but not onto.

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

Show that the function f:N to N given by f (x) =2x is one - one but not onto

The function f : R rarr R defined by f(x) = 7^x + 7^|x| is

Show that the Modulus function f : R to R given by f (x) = [x] is neither one-one nor onto.

Prove that the function f: R to R defined by f(x) = 4x + 3 is invertible and find the inverse of 'f' .