English

If a = {A, B, C} and B = {−2, −1, 0, 1, 2}, Write the Total Number of One-one Functions from a to B.

Advertisements
Advertisements

Question

If A = {abc} and B = {−2, −1, 0, 1, 2}, write the total number of one-one functions from A to B.

Short/Brief Note
Advertisements

Solution

Let F : A → B be a one-one function .

Then , f (a) can take 5 values, f (b) can take 4 values and f (c) can take 3 values .

Then, the number of one-one functions = 5 × 4 × 3 = 60

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Functions - Exercise 2.5 [Page 73]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 2 Functions
Exercise 2.5 | Q 4 | Page 73

RELATED QUESTIONS

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 : Z → Z given by f(x) = x3


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


Show that the function f : R → R given by f(x) = x3 is injective.


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)


If the function `f(x) = sqrt(2x - 3)` is invertible then find its inverse. Hence prove that `(fof^(-1))(x) = x`


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) = sin2x + cos2x


Classify the following function as injection, surjection or bijection :

f : Q → Q, defined by f(x) = x3 + 1


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.


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = 2x + x2 and  g(x) = x3


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = x2 + 8 and g(x) = 3x3 + 1 .


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) = x+1, g(x) = `e^x`

.


Let f(x) = x2 + x + 1 and g(x) = sin x. Show that fog ≠ gof.


If f : R → (−1, 1) defined by `f (x) = (10^x- 10^-x)/(10^x + 10 ^-x)` is invertible, find f−1.


Let f  be a function from C (set of all complex numbers) to itself given by f(x) = x3. Write f−1 (−1).


Let f : R → R+ be defined by f(x) = axa > 0 and a ≠ 1. Write f−1 (x).


If f : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).


The function f : R → R defined by

`f (x) = 2^x + 2^(|x|)` is 

 


 Let
\[g\left( x \right) = 1 + x - \left[ x \right] \text{and} f\left( x \right) = \begin{cases}- 1, & x < 0 \\ 0, & x = 0, \\ 1, & x > 0\end{cases}\] where [x] denotes the greatest integer less than or equal to x. Then for all \[x, f \left( g \left( x \right) \right)\] is equal to


The distinct linear functions that map [−1, 1] onto [0, 2] are


If  \[f\left( x \right) = \sin^2 x\] and the composite function   \[g\left( f\left( x \right) \right) = \left| \sin x \right|\] then g(x) is equal to


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


Let A be a finite set. Then, each injective function from A into itself is not surjective.


Let D be the domain of the real valued function f defined by f(x) = `sqrt(25 - x^2)`. Then, write D


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


If f(x) = (4 – (x – 7)3}, then f–1(x) = ______.


The smallest integer function f(x) = [x] is ____________.


The function f : R → R defined by f(x) = 3 – 4x is ____________.


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


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?

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.

  • Let R: B → G be defined by R = { (b1,g1), (b2,g2),(b3,g1)}, then R is ____________.

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

  • The function f: R → R defined by f(x) = x − 4 is ____________.

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

  • Let f: R → R be defined by f(x) = x − 4. Then the range of f(x) is ____________.

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


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 ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×