English

Every function is invertible. - Mathematics

Advertisements
Advertisements

Question

Every function is invertible.

Options

  • True

  • False

MCQ
True or False

Solution

This statement is False.

Explanation:

Only bijective functions are invertible.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Relations And Functions - Exercise [Page 17]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 1 Relations And Functions
Exercise | Q 61 | Page 17

RELATED QUESTIONS

If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x3 + 5, then find the value of (fog)−1 (x).


Let f : W → W be defined as

`f(n)={(n-1, " if n is odd"),(n+1, "if n is even") :}`

Show that f is invertible a nd find the inverse of f. Here, W is the set of all whole
numbers.


State with reason whether following functions have inverse

f: {1, 2, 3, 4} → {10} with

f = {(1, 10), (2, 10), (3, 10), (4, 10)}


State with reason whether following functions have inverse g: {5, 6, 7, 8} → {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)}


State with reason whether following functions have inverse h: {2, 3, 4, 5} → {7, 9, 11, 13} with h = {(2, 7), (3, 9), (4, 11), (5, 13)}


Show that f: [−1, 1] → R, given by f(x) = `x/(x + 2)`  is one-one. Find the inverse of the function f: [−1, 1] → Range f.

(Hint: For y in Range f, y = `f(x) = x/(x +2)` for some x in [-1, 1] ie x = `2y/(1-y)`


Let fX → Y be an invertible function. Show that f has unique inverse. (Hint: suppose g1 and g2 are two inverses of f. Then for all y ∈ Yfog1(y) = IY(y) = fog2(y). Use one-one ness of f).


Consider f: {1, 2, 3} → {abc} given by f(1) = af(2) = b and f(3) = c. Find f−1 and show that (f−1)−1 = f.


If f→ be given by `f(x) = (3 - x^3)^(1/3)` , then fof(x) is 

(A) `1/(x^3)`

(B) x3

(C) x

(D) (3 − x3)


If f: R → R is defined by f(x) = x2 − 3x + 2, find f(f(x)).


Let f : W → W be defined as f(x) = x − 1 if x is odd and f(x) = x + 1 if x is even. Show that f is invertible. Find the inverse of f, where W is the set of all whole numbers.


If f : R → R, f(x) = x and g: R → R , g(x) =  2x+ 1, and R is the set of real numbers, then find fog(x) and gof (x)


Let f: R → R be defined by f(x) = 3x 2 – 5 and g: R → R by g(x) = `x/(x^2 + 1)` Then gof is ______.


If f(x) = (ax2 + b)3, then the function g such that f(g(x)) = g(f(x)) is given by ____________.


If f : R → R, g : R → R and h : R → R is such that f(x) = x2, g(x) = tanx and h(x) = logx, then the value of [ho(gof)](x), if x = `sqrtpi/2` will be ____________.


Let f : N → R : f(x) = `((2"x"−1))/2` and g : Q → R : g(x) = x + 2 be two functions. Then, (gof) `(3/2)` is ____________.


If f(x) = `(3"x" + 2)/(5"x" - 3)` then (fof)(x) is ____________.


Let f : R → R be the functions defined by f(x) = x3 + 5. Then f-1(x) is ____________.


Let f : R – `{3/5}`→ R be defined by f(x) = `(3"x" + 2)/(5"x" - 3)` Then ____________.


The inverse of the function `"y" = (10^"x" - 10^-"x")/(10^"x" + 10^-"x")` is ____________.


If f : R → R defind by f(x) = `(2"x" - 7)/4` is an invertible function, then find f-1.


Consider the function f in `"A = R" - {2/3}` defiend as `"f"("x") = (4"x" + 3)/(6"x" - 4)` Find f-1.


If f is an invertible function defined as f(x) `= (3"x" - 4)/5,` then f-1(x) is ____________.


If f : R → R defined by f(x) `= (3"x" + 5)/2` is an invertible function, then find f-1.


A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever


Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}

  • Two neighbors X and Y ∈ I. X exercised his voting right while Y did not cast her vote in a general election - 2019. Which of the following is true?

Let 'D' be the domain of the real value function on Ir defined by f(x) = `sqrt(25 - x^2)` the D is :-


Let `f : R {(-1)/3} → R - {0}` be defined as `f(x) = 5/(3x + 1)` is invertible. Find f–1(x).


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×