हिंदी

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

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is True.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Solved Examples [पृष्ठ १०]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 1 Relations And Functions
Solved Examples | Q 33 | पृष्ठ १०

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Show that the function f : R* → R* defined by f(x) = `1/x` is one-one and onto, where R* is the set of all non-zero real numbers. Is the result true, if the domain R* is replaced by N with co-domain being same as R?


Check the injectivity and surjectivity of the following function:

f : N → N given by f(x) = x3


Let fR → be defined as f(x) = 10x + 7. Find the function gR → R such that g o f = f o = 1R.


Show that the function f: ℝ → ℝ defined by f(x) = `x/(x^2 + 1), ∀x in R`is neither one-one nor onto. Also, if g: ℝ → ℝ is defined as g(x) = 2x - 1. Find fog(x)


Which of the following functions from A to B are one-one and onto?
 f1 = {(1, 3), (2, 5), (3, 7)} ; A = {1, 2, 3}, B = {3, 5, 7}


Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : g(x) = |x|  


Show that if f1 and f2 are one-one maps from R to R, then the product f1 × f2 : R → R defined by (f1 × f2) (x) = f1 (x) f2 (x) need not be one - one.


Let f : N → N be defined by

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

Show that f is a bijection. 

                      [CBSE 2012, NCERT]


Let f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3) (4, 9) (5, 9)}. Show that gof and fog are both defined. Also, find fog and gof.


Give examples of two functions f : N → N and g : N → N, such that gof is onto but f is not onto.


Find fog and gof  if : f (x) = x+1, g(x) = `e^x`

.


If f(x) = |x|, prove that fof = f.


If f : R → R be defined by f(x) = x3 −3, then prove that f−1 exists and find a formula for f−1. Hence, find f−1(24) and f−1 (5).


Let f : [−1, ∞) → [−1, ∞) be given by f(x) = (x + 1)2 − 1, x ≥ −1. Show that f is invertible. Also, find the set S = {x : f(x) = f−1 (x)}.


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


Write the domain of the real function f defined by f(x) = `sqrt (25 -x^2)`   [NCERT EXEMPLAR]


If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = \[\alpha x + \beta\]  then find the values of \[\alpha\] and \[ \beta\] . [NCERT EXEMPLAR]


Let\[A = \left\{ x \in R : - 1 \leq x \leq 1 \right\} = \text{B and C} = \left\{ x \in R : x \geq 0 \right\} and\]\[S = \left\{ \left( x, y \right) \in A \times B : x^2 + y^2 = 1 \right\} \text{and } S_0 = \left\{ \left( x, y \right) \in A \times C : x^2 + y^2 = 1 \right\}\]

Then,



Let

 \[A = \left\{ x \in R : x \geq 1 \right\}\] The inverse of the function, 

\[f : A \to A\] given by

\[f\left( x \right) = 2^{x \left( x - 1 \right)} , is\]

 


If  \[F : [1, \infty ) \to [2, \infty )\] is given by

\[f\left( x \right) = x + \frac{1}{x}, then f^{- 1} \left( x \right)\]

 


If  \[f : R \to \left( - 1, 1 \right)\] is defined by

\[f\left( x \right) = \frac{- x|x|}{1 + x^2}, \text{ then } f^{- 1} \left( x \right)\] equals

 


Let f: R → R be the function defined by f(x) = 4x – 3 ∀ x ∈ R. Then write f–1 


Show that the function f: R → R defined by f(x) = `x/(x^2 + 1)`, ∀ ∈ + R , is neither one-one nor onto


Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is ______.


Let f: R → R be defined by f(x) = x2 + 1. Then, pre-images of 17 and – 3, respectively, are ______.


Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not

k = {(1,4), (2, 5)}


Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:

h(x) = x|x|


Using the definition, prove that the function f: A→ B is invertible if and only if f is both one-one and onto


Let g(x) = x2 – 4x – 5, then ____________.


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.

  • The function f: Z → Z defined by f(x) = x2 is ____________.

Consider a function f: `[0, pi/2] ->` R, given by f(x) = sinx and `g[0, pi/2] ->` R given by g(x) = cosx then f and g are


Let f: R→R be a continuous function such that f(x) + f(x + 1) = 2, for all x ∈ R. If I1 = `int_0^8f(x)dx` and I2 = `int_(-1)^3f(x)dx`, then the value of I1 + 2I2 is equal to ______.


`x^(log_5x) > 5` implies ______.


The graph of the function y = f(x) is symmetrical about the line x = 2, then ______.


Let f(x) be a polynomial of degree 3 such that f(k) = `-2/k` for k = 2, 3, 4, 5. Then the value of 52 – 10f(10) is equal to ______.


A function is called into if:


Which condition represents a many-one function?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×