हिंदी

If a = {1, 2, 3} and B = {X, Y}, Then the Number of Functions that Can Be Defined from a into B is (A) 12 (B) 8 (C) 6 (D) 3 - Mathematics

Advertisements
Advertisements

प्रश्न

If A = {1, 2, 3} and B = {xy}, then the number of functions that can be defined from A into B is

विकल्प

  • (a) 12

  • (b) 8

  • (c) 6

  • (d) 3

     
MCQ

उत्तर

(b) 8

Given:
Number of elements in set A = 3
Number of elements in set B = 2
Therefore, the number of functions that can be defined from A into B is = 23 = 8.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Functions - Exercise 3.6 [पृष्ठ ४३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 3 Functions
Exercise 3.6 | Q 10 | पृष्ठ ४३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.


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.

(c) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

 

 


If f(x) = loge (1 − x) and g(x) = [x], then determine function:

(iv) \[\frac{g}{f}\] Also, find (f + g) (−1), (fg) (0),

\[\left( \frac{f}{g} \right) \left( \frac{1}{2} \right), \left( \frac{g}{f} \right) \left( \frac{1}{2} \right)\]
 
 

Let f : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + gf − gfg and \[\frac{f}{g}\] .

 
 

Write the range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .

 

If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]

 

 


If f(x) = cos (log x), then the value of f(xf(y) −\[\frac{1}{2}\left\{ f\left( \frac{x}{y} \right) + f\left( xy \right) \right\}\] is

 

If 2f (x) − \[3f\left( \frac{1}{x} \right) = x^2\] (x ≠ 0), then f(2) is equal to

 

If  \[f\left( x \right) = \frac{\sin^4 x + \cos^2 x}{\sin^2 x + \cos^4 x}\] for x ∈ R, then f (2002) = 


The domain of the function \[f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}\] is

 

Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.

{(1, 0), (3, 3), (2, −1), (4, 1), (2, 2)}


Check if the relation given by the equation represents y as function of x:

2y + 10 = 0


If f(m) = m2 − 3m + 1, find `(("f"(2 + "h") - "f"(2))/"h"), "h" ≠ 0`


Find x, if g(x) = 0 where g(x) = `(5x - 6)/7`


Find x, if g(x) = 0 where g(x) = 6x2 + x − 2


Find the domain and range of the following function.

f(x) = `sqrt((x - 2)(5 - x)`


Express the area A of circle as a function of its radius r


Express the area A of circle as a function of its circumference C.


An open box is made from a square of cardboard of 30 cms side, by cutting squares of length x centimeters from each corner and folding the sides up. Express the volume of the box as a function of x. Also find its domain


lf f(x) = 3(4x+1), find f(– 3)


Prove that `"b"^(log_"b""a"` = a


Select the correct answer from given alternatives.

Let the function f be defined by f(x) = `(2x + 1)/(1 - 3x)` then f–1 (x) is ______.


Select the correct answer from given alternatives

If f(x) = 2x2 + bx + c and f(0) = 3 and f(2) = 1, then f(1) is equal to


Select the correct answer from given alternative.

The domain and range of f(x) = 2 − |x − 5| is


Answer the following:

Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0


Answer the following:

Find the range of the following function.

f(x) = [x] – x


Given the function f: x → x2 – 5x + 6, evaluate f(– 1)


The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.

Length ‘x’ of
forehand (in cm)
Height 'y' 
(in inches)
35 56
45 65
50 69.5
55 74

Find a and b


The domain of the function f(x) = `sqrtx` is ______.


The range of the function f(x) = `(x^2 - 3x + 2)/(x^3 - 4x^2 + 5x - 2)` is ______


Domain of function f(x) = cos–1 6x is ______.


Find the domain of the function f given by f(x) = `1/sqrt([x]^2 - [x] - 6)`


Find the domain of the following functions given by f(x) = x|x|


Let f(x) = `sqrt(x)` and g(x) = x be two functions defined in the domain R+ ∪ {0}. Find (fg)(x)


The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.


The range of the function y = `1/(2 - sin3x)` is ______.


If f(x) = x3 – 1 and domain of f = {0, 1, 2, 3}, then domain of f–1 is ______.


The function f: R `rightarrow` R defined by f(x) = sin x is ______.


Which of the following functions is NOT one-one?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×