मराठी

Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one.

Advertisements
Advertisements

प्रश्न

Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Show that f is one-one.

बेरीज
Advertisements

उत्तर

It is given that A = {1, 2, 3}, B = {4, 5, 6, 7}.

f: A → B is defined as f = {(1, 4), (2, 5), (3, 6)}.

∴ f(1) = 4, f(2) = 5 and f(3) = 6

It is seen that the images of distinct elements of A under f are distinct.

Hence, function f is one-one.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations and Functions - EXERCISE 1.2 [पृष्ठ ११]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 1 Relations and Functions
EXERCISE 1.2 | Q 6. | पृष्ठ ११

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

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 S = {a, b, c} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists.

F = {(a, 2), (b, 1), (c, 1)}


Let f: R → R be the Signum Function defined as

f(x) = `{(1,x>0), (0, x =0),(-1, x< 0):}`

and g: R → R be the Greatest Integer Function given by g(x) = [x], where [x] is greatest integer less than or equal to x. Then does fog and gof coincide in (0, 1]?


Classify the following function as injection, surjection or bijection :  f : Z → Z given by f(x) = x2


Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = sin2x + cos2x


Set of ordered pair of a function ? If so, examine whether the mapping is injective or surjective :{(a, b) : a is a person, b is an ancestor of a} 


Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.


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


Verify associativity for the following three mappings : f : N → Z0 (the set of non-zero integers), g : Z0 → Q and h : Q → R given by f(x) = 2x, g(x) = 1/x and h(x) = ex.


State with reason whether the following functions have inverse:

h : {2, 3, 4, 5} → {7, 9, 11, 13} with h = {(2, 7), (3, 9), (4, 11), (5, 13)}


Find f −1 if it exists : f : A → B, where A = {1, 3, 5, 7, 9}; B = {0, 1, 9, 25, 49, 81} and f(x) = x2


Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f−1


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.


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


If A = {1, 2, 3} and B = {a, b}, write the total number of functions from A to B.


Write the total number of one-one functions from set A = {1, 2, 3, 4} to set B = {a, b, c}.


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


If f : R → R defined by f(x) = 3x − 4 is invertible, then write f−1 (x).


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


Write the domain of the real function

`f (x) = 1/(sqrt([x] - x)`.


Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. State whether f is one-one or not.


A function f  from the set of natural numbers to integers defined by

`{([n-1]/2," when  n is  odd"   is ),(-n/2,when  n  is  even ) :}`

 

 


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 \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.


Mark the correct alternative in the following question:
Let f : R→ R be defined as, f(x) =  \[\begin{cases}2x, if x > 3 \\ x^2 , if 1 < x \leq 3 \\ 3x, if x \leq 1\end{cases}\] 

Then, find f( \[-\]1) + f(2) + f(4)

 


Write about strcmp() function.


If f: R → R is defined by f(x) = x2 – 3x + 2, write f(f (x))


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

h(x) = x|x|


The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is ____________.


If N be the set of all-natural numbers, consider f: N → N such that f(x) = 2x, ∀ x ∈ N, then f is ____________.


An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions.

  • Ravi wants to know among those relations, how many functions can be formed from B to G?

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


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


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



The given function f : R → R is not ‘onto’ function. Give reason.


Let f: R→Rbe defined as f (x) = `(x^2 + 1)/2`, then ______.


Let \(X=\{-1,2,5,8,11\}\), \(Y=\{4,6,8\}\), and suppose different elements \(2,5,8\) of \(X\) have the same image \(4\). What type of function is it with respect to the one-one property?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×