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If X = {1, 2, 3, 4}, Y = {1, 2, 3,…., 20}, and f: X → Y be the correspondence which assigns each element in X the value equal to its square, then the domain, codomain and range of f is
The correct option is B
Since the function is defined from
XY.So the domain will be the set X which is {1,2,3,4}. Codomain is what may possibly come out of a function. So codomain is the whole set Y which is {1,2,3,...,20}. Range is The range is the set of possible output values which will be the values in the set of Y which have a preimage. That is, the value of squares. So the range is {1,4,,9,16}.
A relation f from a set A to a set B is said to be function if every element of set A has one and only one image in set B. In other words, a function f is a relation such that no two pairs in the relation has the same first element. The notation f : X →Y means that f is a function from X to Y.
4  x^{2} = 0
=> (2+x)(2x) = 0
x = +2
Now select a test point, let it be x = 0. Then y = (4  (0)^{2})^{1/2} = 2, so the function is defined on [2,2]
Thus, the graph of y = (4  x^{2})^{1/2} is a semicircle with radius 2 and domain is [2,2]
Let X = {1, 2, 3, 4}, Y = {1, 2, …, 10} and f : X –> Y be defined by f(x) = 2x + 1, x ∈ X. Then the range of f is
X = {1, 2, 3, 4}
Y = {1, 2, …, 10}
f: X→ Y be defined by
f(x) = 2x + 1
f (1) = 3
f (2) = 5
f (3) = 7
f (4) = 9
Range(f) = {3, 5, 7, 9}
If f(x) = x^{2} – x + 1; g(x) = 7x – 3, be two real functions then (f + g)(3) is
f(x) = x2 – x + 1; g(x) = 7x – 3
(f+g)(x) = (x2  x + 1 + 7x  3)
=(x^{2}  x + 7x + 1  3)
= x^{2} + 6x  2
(f+g)(3) = x^{2} + 6x  2
= (3)^{2} + 6(3)  2
= 9 + 18  2
= 25
A function is a relation in which no two ordered pairs have the same first element. A function associates each element in its domain with one and only one element in its range. R={(1,2), (1,4)(3,1),(5,1)} is not a function because all the first elements are not different.
The following arrow diagram of the function f : A → A be defined as
If A = {1,2,3}, B = {a,b,c}, which of the following is a function?
Option A has value b & c for 2.
Option C has value b & c for 1.
Option D has value a & c for 1.
Example: y = x^{2}.
If x = 2, y = 4.
If x = 2, y = 4. So there you have a manytoone relation and it is DEFINITELY a function.
Now, a onetomany relation is NOT a function.
The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}
Identify the domain and range of the function f(x), defined in N, as below:
If A = {2, 4, 6, 8} and B = {2, 3, 5, 7, 9}. Which of the following is a function from A to B?
f(x) = 3x/2x8
denominator can't be zero so
2x  8 not equal to 0
x should not equal to 4
we have domain R  {4}
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156 videos176 docs132 tests
