English

The composition of functions is associative.

Advertisements
Advertisements

Question

The composition of functions is associative.

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is True.

Explanation:

fo(goh)(x) = (fog)oh

This can be verified by considering particular f(x), g(x) and h(x)

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

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 1 Relations And Functions
Exercise | Q 60 | 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).


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


Consider f: R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.


Consider f: R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f−1 of given f by `f^(-1)(y) = sqrt(y - 4)`, where R+ is the set of all non-negative real numbers.


Consider f: R+ → [–5, ∞) given by f(x) = 9x2 + 6x – 5. Show that f is invertible with `f^(-1)(y) = ((sqrt(y + 6) - 1)/3)`.


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


Consider f: `R_+ -> [-5, oo]` given by `f(x) = 9x^2 + 6x - 5`. Show that f is invertible with `f^(-1) (y) ((sqrt(y + 6)-1)/3)`

Hence Find

1) `f^(-1)(10)`

2) y if `f^(-1) (y) = 4/3`

where R+ is the set of all non-negative real 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: R → R be defined by f(x) = 3x 2 – 5 and g: R → R by g(x) = `x/(x^2 + 1)` Then gof is ______.


Let f: R → R be the function defined by f(x) = sin (3x+2) ∀ x ∈ R. Then f is invertible.


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


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 ____________.


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 ____________.


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


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?

`f : x -> sqrt((3x^2 - 1)` and `g : x -> sin (x)` then `gof : x ->`?


If `f(x) = 1/(x - 1)`, `g(x) = 1/((x + 1)(x - 1))`, then the number of integers which are not in domian of gof(x) are


Let A = `{3/5}` and B = `{7/5}` Let f: A → B: f(x) = `(7x + 4)/(5x - 3)` and g:B → A: g(y) = `(3y + 4)/(5y - 7)` then (gof) is equal to


If f: N → Y be a function defined as f(x) = 4x + 3, Where Y = {y ∈ N: y = 4x+ 3 for some x ∈ N} then function is


If f(x) = [4 – (x – 7)3]1/5 is a real invertible function, then find f–1(x).


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


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


What is the necessary and sufficient condition for a function to be invertible?


Which equation expresses that applying a function and then its inverse returns the original input?


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


Which sequence gives the standard method to find an inverse of a function?


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


For \(f:\mathbb{R}\to\mathbb{R}\) defined by \(f(x)=10x+7\), which function satisfies \(g\circ f=f\circ g=I_R\)?


What are the domain and range of the inverse function in the graphical example?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×