हिंदी

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. - Mathematics

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. State whether f is one-one or not.

Advertisements

उत्तर

f = {(1, 4), (2, 5), (3, 6)}
Here, different elements of the domain have different images in the co-domain.
So, f is one-one .

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Functions - Exercise 2.5 [पृष्ठ ७४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 2 Functions
Exercise 2.5 | Q 36 | पृष्ठ ७४

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Show that the function f in `A=R-{2/3} ` defined as `f(x)=(4x+3)/(6x-4)` is one-one and onto hence find f-1


Check the injectivity and surjectivity of the following function:

f : N → N given by f(x) = x3


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


Let fR → R be the Signum Function defined as

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

and gR → 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 : N → N given by f(x) = x2


Classify the following function as injection, surjection or bijection : f : N → N given by f(x) = x3


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


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.


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


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


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


if f (x) = `sqrt (x +3) and  g (x) = x ^2 + 1` be two real functions, then find fog and gof.


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


A function f : R → R is defined as f(x) = x3 + 4. Is it a bijection or not? In case it is a bijection, find f−1 (3).


Let f : R `{- 4/3} `- 43 →">→ R be a function defined as f(x) = `(4x)/(3x +4)` . Show that f : R - `{-4/3}`→ Rang (f) is one-one and onto. Hence, find f -1.


If f : R → R is given by f(x) = x3, write f−1 (1).


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 be defined by f(x) = x4, write f−1 (1).

Write the domain of the real function

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


If the mapping f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3}, given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, then write fog. [NCERT EXEMPLAR]


Let

\[f : R \to R\]
\[f\left( x \right) = \frac{x^2 - 8}{x^2 + 2}\]
Then,  f is


Let A = R − (2) and B = R − (1). If f: A ⟶ B is a function defined by`"f(x)"=("x"-1)/("x"-2),` how that f is one-one and onto. Hence, find f−1


Write about strlen() function.


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


Let R be the set of real numbers and f: R → R be the function defined by f(x) = 4x + 5. Show that f is invertible and find f–1.


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.


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)}


If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is ______.


Let f: R → R be defined by f(x) = `1/x` ∀ x ∈ R. Then f is ______.


Let f: R → R be the functions defined by f(x) = x3 + 5. Then f–1(x) is ______.


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


The function f: R → R defined as f(x) = x3 is:


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.


Number of integral values of x satisfying the inequality `(3/4)^(6x + 10 - x^2) < 27/64` is ______.


Let a and b are two positive integers such that b ≠ 1. Let g(a, b) = Number of lattice points inside the quadrilateral formed by lines x = 0, y = 0, x = b and y = a. f(a, b) = `[a/b] + [(2a)/b] + ... + [((b - 1)a)/b]`, then the value of `[(g(101, 37))/(f(101, 37))]` is ______.

(Note P(x, y) is lattice point if x, y ∈ I)

(where [.] denotes greatest integer function)


Let f(x) = ax (a > 0) be written as f(x) = f1(x) + f2(x), where f1(x) is an even function and f2(x) is an odd function. Then f1(x + y) + f1(x – y) equals ______.


Let f(n) = `[1/3 + (3n)/100]n`, where [n] denotes the greatest integer less than or equal to n. Then `sum_(n = 1)^56f(n)` is equal to ______.


Let f(x) be a polynomial function of degree 6 such that `d/dx (f(x))` = (x – 1)3 (x – 3)2, then

Assertion (A): f(x) has a minimum at x = 1.

Reason (R): When `d/dx (f(x)) < 0, ∀  x ∈ (a - h, a)` and `d/dx (f(x)) > 0, ∀  x ∈ (a, a + h)`; where 'h' is an infinitesimally small positive quantity, then f(x) has a minimum at x = a, provided f(x) is continuous at x = a.


ASSERTION (A): The relation f : {1, 2, 3, 4} `rightarrow` {x, y, z, p} defined by f = {(1, x), (2, y), (3, z)} is a bijective function.

REASON (R): The function f : {1, 2, 3} `rightarrow` {x, y, z, p} such that f = {(1, x), (2, y), (3, z)} is one-one.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×