Advertisements
Advertisements
Question
Let A and B be any two sets such that n(B) = p, n(A) = q then the total number of functions f : A → B is equal to ______.
Solution
Let A and B be any two sets such that n(B) = p, n(A) = q then the total number of functions f : A → B is equal to pq functions.
Explanation:
Any element of set A
Say xi can be connected with the element of set B in p ways.
Hence, there are exactly pq functions.
APPEARS IN
RELATED QUESTIONS
Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the set are functions from X to Y.
(b) f2 = {(1, 1), (2, 7), (3, 5)}
If \[f\left( x \right) = \begin{cases}x^2 , & \text{ when } x < 0 \\ x, & \text{ when } 0 \leq x < 1 \\ \frac{1}{x}, & \text{ when } x \geq 1\end{cases}\]
find: (a) f(1/2), (b) f(−2), (c) f(1), (d)
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(v) \[\frac{g}{f}\]
If f(x) = loge (1 − x) and g(x) = [x], then determine function:
(iii) \[\frac{f}{g}\]
Write the domain and range of function f(x) given by \[f\left( x \right) = \sqrt{\left[ x \right] - x}\] .
Let A = {1, 2, 3} and B = {2, 3, 4}. Then which of the following is a function from A to B?
If f(x) = cos (log x), then the value of f(x) f(y) −\[\frac{1}{2}\left\{ f\left( \frac{x}{y} \right) + f\left( xy \right) \right\}\] is
Which of the following are functions?
If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(2)
If f(m) = m2 − 3m + 1, find `f(1/2)`
Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x
Find the domain and range of the following function.
g(x) = `(x + 4)/(x - 2)`
Check the injectivity and surjectivity of the following function.
f : Z → Z given by f(x) = x2
Express the following logarithmic equation in exponential form
In `1/2` = – 0.693
Write the following expression as sum or difference of logarithm
In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`
Select the correct answer from given alternatives.
If log (5x – 9) – log (x + 3) = log 2 then x = ...............
Answer the following:
If a2 + b2 = 7ab, show that, `log(("a" + "b")/3) = 1/2 log "a" + 1/2 log "b"`
Answer the following:
If `log"a"/(x + y - 2z) = log"b"/(y + z - 2x) = log"c"/(z + x - 2y)`, show that abc = 1
Answer the following:
Find the domain of the following function.
f(x) = 5–xPx–1
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - x^2) + sqrt(5 - x)`
Given the function f: x → x2 – 5x + 6, evaluate f(2)
A graph representing the function f(x) is given in it is clear that f(9) = 2
Find the following values of the function
(a) f(0)
(b) f(7)
(c) f(2)
(d) f(10)
Find the domain for which the functions f(x) = 2x2 – 1 and g(x) = 1 – 3x are equal.
Find the range of the following functions given by `|x - 4|/(x - 4)`
Find the range of the following functions given by `sqrt(16 - x^2)`
Redefine the function which is given by f(x) = `|x - 1| + |1 + x|, -2 ≤ x ≤ 2`
Find the domain of the following functions given by f(x) = `1/sqrt(1 - cos x)`
