Advertisements
Advertisements
Question
Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.
Advertisements
Solution
We know that every onto function from A to itself is one-one.
So, the number of one-one functions = number of bijections = n!
APPEARS IN
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
Prove that the greatest integer function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
Give an example of a function which is neither one-one nor onto ?
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
Classify the following function as injection, surjection or bijection :
f : Q − {3} → Q, defined by `f (x) = (2x +3)/(x-3)`
Show that the exponential function f : R → R, given by f(x) = ex, is one-one but not onto. What happens if the co-domain is replaced by`R0^+` (set of all positive real numbers)?
Find gof and fog when f : R → R and g : R → R is defined by f(x) = 8x3 and g(x) = x1/3.
Find fog and gof if : f (x) = x2 g(x) = cos x .
Find fog and gof if : f (x) = |x|, g (x) = sin x .
If f : R → R be defined by f(x) = x3 −3, then prove that f−1 exists and find a formula for f−1. Hence, find f−1(24) and f−1 (5).
Which of the following graphs represents a one-one function?

If f : R → R is given by f(x) = x3, write f−1 (1).
If f : C → C is defined by f(x) = x4, write f−1 (1).
Let \[f : \left( - \frac{\pi}{2}, \frac{\pi}{2} \right) \to R\] be a function defined by f(x) = cos [x]. Write range (f).
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 : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).
If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = \[\alpha x + \beta\] then find the values of \[\alpha\] and \[ \beta\] . [NCERT EXEMPLAR]
The function \[f : [0, \infty ) \to \text {R given by } f\left( x \right) = \frac{x}{x + 1} is\]
The function
Let \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] Then, for what value of α is \[f \left( f\left( x \right) \right) = x?\]
Mark the correct alternative in the following question:
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
Which function is used to check whether a character is alphanumeric or not?
Write about strlen() function.
Write about strcmp() function.
Consider the set A containing n elements. Then, the total number of injective functions from A onto itself is ______
Let A be a finite set. Then, each injective function from A into itself is not surjective.
Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.
{(x, y): x is a person, y is the mother of x}
Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x4, is ____________.
Let f : R `->` R be a function defined by f(x) = x3 + 4, then f is ______.
Let f: R → R defined by f(x) = x4. Choose the correct answer
The domain of the function `cos^-1((2sin^-1(1/(4x^2-1)))/π)` is ______.
The domain of function is f(x) = `sqrt(-log_0.3(x - 1))/sqrt(x^2 + 2x + 8)` is ______.
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 ______.
The trigonometric equation tan–1x = 3tan–1 a has solution for ______.
