हिंदी

For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is injective. Then both f and g are injective functions.

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प्रश्न

For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is injective. Then both f and g are injective functions.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
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उत्तर

This statement is False.

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अध्याय 1: Relations And Functions - Solved Examples [पृष्ठ १०]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 1 Relations And Functions
Solved Examples | Q 32 | पृष्ठ १०

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Check the injectivity and surjectivity of the following function:

f : N → N given by f(x) = x3


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In the following case, state whether the function is one-one, onto or bijective. Justify your answer.

f : R → R defined by f(x) = 3 – 4x


Let f : R → R be defined as f(x) = 3x. Choose the correct answer.


Give examples of two surjective functions f1 and f2 from Z to Z such that f1 + f2 is not surjective.


Find gof and fog when f : R → R and g : R → R is defined by f(x) = 2x + 3 and  g(x) = x2 + 5 .


Let f = {(1, −1), (4, −2), (9, −3), (16, 4)} and g = {(−1, −2), (−2, −4), (−3, −6), (4, 8)}. Show that gof is defined while fog is not defined. Also, find gof.


Let f(x) = x2 + x + 1 and g(x) = sin x. Show that fog ≠ gof.


Let f be a real function given by f (x)=`sqrt (x-2)`
Find each of the following:

(i) fof
(ii) fofof
(iii) (fofof) (38)
(iv) f2

Also, show that fof ≠ `f^2` .


 If f, g : R → R be two functions defined as f(x) = |x| + x and g(x) = |x|- x, ∀x∈R" .Then find fog and gof. Hence find fog(–3), fog(5) and gof (–2).


Find f −1 if it exists : f : A → B, where A = {0, −1, −3, 2}; B = {−9, −3, 0, 6} and f(x) = 3 x.


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


Which of the following graphs represents a one-one function?


If f : R → R is defined by f(x) = x2, write f−1 (25)


Let C denote the set of all complex numbers. A function f : C → C is defined by f(x) = x3. Write f−1(1).


If f : R → R is defined by f(x) = x2, find f−1 (−25).


If f : R → Rg : R → are given by f(x) = (x + 1)2 and g(x) = x2 + 1, then write the value of fog (−3).


Let f be an invertible real function. Write ( f-1  of ) (1) + ( f-1  of ) (2) +..... +( f-1 of ) (100 )


Let A = {1, 2, 3, 4} and B = {ab} be two sets. Write the total number of onto functions from A to B.


Write the domain of the real function

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Write whether f : R → R, given by `f(x) = x + sqrtx^2` is one-one, many-one, onto or into.


Let 

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If the function\[f : R \to \text{A given by} f\left( x \right) = \frac{x^2}{x^2 + 1}\] is a surjection, then A =

 

 


If \[g \left( f \left( x \right) \right) = \left| \sin x \right| \text{and} f \left( g \left( x \right) \right) = \left( \sin \sqrt{x} \right)^2 , \text{then}\]

 


If  \[g\left( x \right) = x^2 + x - 2\text{ and} \frac{1}{2} gof\left( x \right) = 2 x^2 - 5x + 2\] is equal to


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Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.

Answer the following questions using the above information.

  • Let : N → R be defined by f(x) = x2. Range of the function among the following is ____________.

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.

Answer the following questions using the above information.

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Many students choosing the same favourite subject resembles which type of function?


A perfect one-to-one matching between users and unique IDs is similar to:


Which condition represents a one-one (injective) function?


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