हिंदी

Let N be the set of natural numbers and the function f: N → N be defined by f(n) = 2n + 3 ∀ n ∈ N. Then f is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

Let N be the set of natural numbers and the function f: N → N be defined by f(n) = 2n + 3 ∀ n ∈ N. Then f is ______.

विकल्प

  • Surjective

  • Injective

  • Bijective

  • None of these

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

Let N be the set of natural numbers and the function f: N → N be defined by f(n) = 2n + 3 ∀ n ∈ N. Then f is injective.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Solved Examples [पृष्ठ ८]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 1 Relations And Functions
Solved Examples | Q 19 | पृष्ठ ८

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Let A = R − {3} and B = R − {1}. Consider the function f : A → B defined by f(x) = `((x- 2)/(x -3))`. Is f one-one and onto? Justify your answer.


Show that the function f : R → {x ∈ R : −1 < x < 1} defined by f(x) = `x/(1 + |x|)`, x ∈ R is one-one and onto function.


Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = 3 − 4x


Show that the function f : R − {3} → R − {2} given by f(x) = `(x-2)/(x-3)` is a bijection.


Give examples of two one-one functions f1 and f2 from R to R, such that f1 + f2 : R → R. defined by (f1 + f2) (x) = f1 (x) + f2 (x) is not one-one.


Let A = {abc}, B = {u vw} and let f and g be two functions from A to B and from B to A, respectively, defined as :
f = {(av), (bu), (cw)}, g = {(ub), (va), (wc)}.
Show that f and g both are bijections and find fog and gof.


Let f : R → R and g : R → R be defined by f(x) = x2 and g(x) = x + 1. Show that fog ≠ gof.


If f : A → B and g : B → C are onto functions, show that gof is a onto function.


Find fog and gof  if : f(x) = c, c ∈ R, g(x) = sin `x^2`


Consider f : {1, 2, 3} → {abc} and g : {abc} → {apple, ball, cat} defined as f (1) = af (2) = bf (3) = cg (a) = apple, g (b) = ball and g (c) =  cat. Show that fg and gof are invertible. Find f−1g−1 and gof−1and show that (gof)−1 = f 1o g−1


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


If f : C → C is defined by f(x) = (x − 2)3, write f−1 (−1).


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


The range of the function

\[f\left( x \right) =^{7 - x} P_{x - 3}\]

 


Which of the following functions from

\[A = \left\{ x : - 1 \leq x \leq 1 \right\}\]

to itself are bijections?

 

 

 


Let

\[A = \left\{ x : - 1 \leq x \leq 1 \right\} \text{and} f : A \to \text{A such that f}\left( x \right) = x|x|\]

 


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 \[f : R \to R is given by f\left( x \right) = 3x - 5, then f^{- 1} \left( x \right)\] 

 


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

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

 


Let  \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] Then, for what value of α is \[f \left( f\left( x \right) \right) = x?\]

 


Let 
\[f : R \to R\]  be given by \[f\left( x \right) = x^2 - 3\] Then, \[f^{- 1}\] is given by 

 


Mark the correct alternative in the following question:
If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is


Mark the correct alternative in the following question:
Let f :  \[-\] \[\left\{ \frac{3}{5} \right\}\] \[\to\]  R be defined by f(x) = \[\frac{3x + 2}{5x - 3}\] Then,

 


Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of surjections from A into B is ______.


Let A = R – {3}, B = R – {1}. Let f : A → B be defined by `"f"("x") = ("x" - 2)/("x" - 3)` Then, ____________.


Range of `"f"("x") = sqrt((1 - "cos x") sqrt ((1 - "cos x")sqrt ((1 - "cos x")....infty))`


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 f: {1,2,3,....} → {1,4,9,....} be defined by f(x) = x2 is ____________.

If f: R → R given by f(x) =(3 − x3)1/3, find f0f(x)


Let f: R → R defined by f(x) = x4. Choose the correct answer


Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if  "n is even"):}` Is the function injective? Justify your answer.


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 ______.


The solution set of the inequation log1/3(x2 + x + 1) + 1 > 0 is ______.


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


For x ∈ R, x ≠ 0, let f0(x) = `1/(1 - x)` and fn+1 (x) = f0(fn(x)), n = 0, 1, 2, .... Then the value of `f_100(3) + f_1(2/3) + f_2(3/2)` is equal to ______.


Which one of the following graphs is a function of x?

Graph A Graph B

The trigonometric equation tan–1x = 3tan–1 a has solution for ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×