Relations and Functions - Online Test
Q1. Let A = {1, 2, 3} and B = {2, 3, 4}, then which of the following is a function from A to B?
Answer : Option B
Explaination / Solution:
{(1, 3), (2, 3), (3, 3)} is a function ,because for each x ∈ A , there is a unique y ∈ B such that ( x , y) ∈f., i.e. xfy.
Q2. The diagram given below shows that
Answer : Option A
Explaination / Solution:
Because , an object in domain cann’t have two images in its co-domain.
Q3. The domain of the function f = {(1,3), (3,5), (2,6)} is
Answer : Option B
Explaination / Solution:
The domain in ordered pair (x,y) is represented by x-co ordinate . Therefore, the domain of the given function is given by : { 1 , 3 , 2 }.
Q4. The range of the function f(x) =|x−1| is
Answer : Option C
Explaination / Solution:
We have , f(x) =|x−1|, which always gives non-negative values of f(x) for all x∈R.Therefore range of the given function is all non-negative real numbers i.e. [0,∞] .
Q5.
The function
Answer : Option C
Explaination / Solution:
Because , here f( - x ) = - f( x).Therefore , the given function is an even function.
Q6. The domain of definition of the function y=f(x)= √−x is :
Answer : Option A
Explaination / Solution:
y is defined if −x ⩾ 0 ,i.e.if x ⩽ 0, i.e. x ∈(−∞,0].
Q7. The range of the function f(x) = [sin x] is
Answer : Option B
Explaination / Solution:
The only possible integral values of sin x are { -1 ,0, 1 }.As −1≤sinθ≤1
Q8. The range of the function f(x) = x – [x] is
Answer : Option C
Explaination / Solution:
Since [x] ≤ x, therefore , x – [x] ≥ 0. Also, x – [x] <1,∴0⩽x−[x]<1. Therefore ,Range of f = [0,1).
Q9. The domain of the function
Answer : Option C
Explaination / Solution:
The domain of the function f(x) is all reals,because f(x) is defined for all real values of x.
Q10. The range of function f(x) = [x] is :
Answer : Option D
Explaination / Solution:
integral part of x.
