Home
Class 12
MATHS
Prove that the function f: N to Y define...

Prove that the function `f: N to Y` defined by `f(x) = x^(2)`, where `y = {y : y = x^(2) , x in N}` is invertible. Also write the inverse of f(x).

Text Solution

Verified by Experts

The correct Answer is:
f is invertible with `f^(-1) = g`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise TRY YOURSELF - EXERCISE (One mark questions)|5 Videos

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise TRY YOURSELF - EXERCISE (Two marks questions)|5 Videos

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise THREE MARKS QUESTIONS WITH ANSWERS|16 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

Verify whether the function f : N to Y defined by f(x) = 4x + 3 , where Y = {y : y = 4x + 3, x in N} is invertible or not. Write the inverse of f(x) if exists.

Prove that the function f:N to Y defined by f(x) = 4x +3 , where Y=[y:y =4x +3,x in N] is invertible . Also write inverse of f(x).

The function f(x) is defined by f(x) = (x+2)e^(-x) is

Prove that the function f : R to R defined by f(x) = 2x , AA x in R is bijective.

Show that the function f : N to N defined by f(x) = x^(2), AA x in N is injective but not surjective.

Let R+ be the set of all non-negative real number. Show that the faction f : R, to [4, oo) defined f(x) = x^(2) + 4 is invertible. Also write the inverse of f.

Let f: N rarr N be defined by f(x)=x^(2)+x+1 then f is

Let f : N to R be defined by f(x) = 4x^(2) + 12x + 15 , show that f: N to S , where S is the function, is invertible. Also find the inverse.

Show that the function f : N to N defined by f(x) = x^(3), AA x in N is injective but not surjective.

The function defined by y = x^(2) is