हिंदी

Every function is invertible.

Advertisements
Advertisements

प्रश्न

Every function is invertible.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is False.

Explanation:

Only bijective functions are invertible.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Exercise [पृष्ठ १७]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 1 Relations And Functions
Exercise | Q 61 | पृष्ठ १७

वीडियो ट्यूटोरियलVIEW ALL [4]

संबंधित प्रश्न

Let f, g and h be functions from R to R. Show that

(f + g)oh = foh + goh

(f · g)oh = (foh)·(goh)


Find gof and fog, if f(x) = 8x3 and `g(x) = x^(1/3)`.


If `f(x) = (4x + 3)/(6x - 4), x ≠ 2/3` show that fof(x) = x, for all `x ≠ 2/3`. What is the inverse of f?


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] i.e., `x = (2y)/(1 - y)`)


Let f: X → 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 ∈ Y, fog1(y) = IY(y) = fog2(y). Use one-one ness of f).


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


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


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.


Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? If g is described by g (x) = αx + β, then what value should be assigned to α and β


Let f: [0, 1] → [0, 1] be defined by f(x) = `{{:(x",",  "if"  x  "is rational"),(1 - x",",  "if"  x  "is irrational"):}`. Then (f o f) x is ______.


Let f = {(1, 2), (3, 5), (4, 1) and g = {(2, 3), (5, 1), (1, 3)}. Then g o f = ______ and f o g = ______.


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 ____________.


If f : R → R, g : R → R and h : R → R are such that f(x) = x2, g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 will be ____________.


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?

The domain of definition of f(x) = log x2 – x + 1) (2x2 – 7x + 9) is:-


Domain of the function defined by `f(x) = 1/sqrt(sin^2 - x) log_10 (cos^-1 x)` is:-


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


Which statement correctly describes a one-one (injective) function?


A function that is both one-one and onto is called what?


Which property of inverse functions is represented by \((f^{-1})^{-1}=f\)?


If \(f:A\to B\) and \(g:B\to C\) are both bijections, which statement is the Reversal Law of Inverses?


According to the Reflective Property, the graph of \(f^{-1}\) is the exact reflection of the graph of \(f\) across which line?


A function is called a self-inverse function when which condition holds?


For \(f:\mathbb{R}\to(-1,1)\) defined by \(f(x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}\), what is \(f^{-1}(x)\)?


In the graphical example, what are the domain and range of the given function?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×