हिंदी

Write the Total Number of One-one Functions from Set a = {1, 2, 3, 4} to Set B = {A, B, C}.

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

A has 4 elements and B has 3 elements.
Also, one-one function is only possible from A to B if (A) ≤ n (B).
But, here n B if (A) > n (B).
So, the number of one-one functions from A to B is 0.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Functions - Exercise 2.5 [पृष्ठ ७३]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 2 Functions
Exercise 2.5 | Q 5 | पृष्ठ ७३

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

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, 3), (b, 2), (c, 1)} 


Give an example of a function which is one-one but not onto ?


Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = |x|


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = x and g(x) = |x| .


Let A = {a, b, c}, B = {u v, w} and let f and g be two functions from A to B and from B to A, respectively, defined as :
f = {(a, v), (b, u), (c, w)}, g = {(u, b), (v, a), (w, c)}.
Show that f and g both are bijections and find fog and gof.


If f(x) = 2x + 5 and g(x) = x2 + 1 be two real functions, then describe each of the following functions:
(1) fog
(2) gof
(3) fof
(4) f2
Also, show that fof ≠ f2


Let f, g, h be real functions given by f(x) = sin x, g (x) = 2x and h (x) = cos x. Prove that fog = go (fh).


Let  f  be any real function and let g be a function given by g(x) = 2x. Prove that gof = f + f.


State with reason whether the following functions have inverse :
f : {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}


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


Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.


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.


Let f be a function from R to R, such that f(x) = cos (x + 2). Is f invertible? Justify your answer.


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 `f : R - {- 3/5}` → R be a function defined as `f  (x) = (2x)/(5x +3).` 

f-1 : Range of f → `R -{-3/5}`.


If f(x) = x + 7 and g(x) = x − 7, x ∈ R, write fog (7).


Let

\[f : [2, \infty ) \to X\] be defined by

\[f\left( x \right) = 4x - x^2\] Then, f is invertible if X =

 


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

 


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

 


Write about strcmp() function.


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.


The domain of the function f: R → R defined by f(x) = `sqrt(x^2 - 3x + 2)` is ______


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 X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x4, 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 ____________.

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


Function f: R → R, defined by f(x) = `x/(x^2 + 1)` ∀ x ∈ R is not


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


Let x is a real number such that are functions involved are well defined then the value of `lim_(t→0)[max{(sin^-1  x/3 + cos^-1  x/3)^2, min(x^2 + 4x + 7)}]((sin^-1t)/t)` where [.] is greatest integer function and all other brackets are usual brackets.


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)


The domain of function is f(x) = `sqrt(-log_0.3(x - 1))/sqrt(x^2 + 2x + 8)` is ______.


Let f(1, 3) `rightarrow` R be a function defined by f(x) = `(x[x])/(1 + x^2)`, where [x] denotes the greatest integer ≤ x, Then the range of f is ______.


If A = {x ∈ R: |x – 2| > 1}, B = `{x ∈ R : sqrt(x^2 - 3) > 1}`, C = {x ∈ R : |x – 4| ≥ 2} and Z is the set of all integers, then the number of subsets of the set (A ∩ B ∩ C) C ∩ Z is ______.


Let S = {1, 2, 3, 4, 5, 6, 7}. Then the number of possible functions f: S `rightarrow` S such that f(m.n) = f(m).f(n) for every m, n ∈ S and m.n ∈ S is equal to ______.


Write the domain and range (principle value branch) of the following functions:

f(x) = tan–1 x.


A function is onto when every element of the codomain has:


Which condition represents an onto (surjective) function?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×