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Relation & Functions

Theory and Formula

Question


Q1. The range of {(2,10)(3,10)(4,10)} is .

(a) 2 (b) 4 (c) 3 (d) 10

Solution.
(d) 10
Solution

Q2. In identity function Domain is equal to

(a) 0 (b) Range (c) 1 (d) ∞

Solution.
(b) Range
Solution

Q3. If A = {3,4,5}, B = {6,7,8,10} and f = {(3,6)(4,7)(5,8)} is a function from A to B , f is one-one or not

(a) Yes (b) No (c) Can't say

Solution.
(a) Yes
Solution

Q4. Domain and Range of the identity function are ____________.

(a) both are equal to R. (b) both are not equal (c) None of these

Solution.
(a) both are equal to R.
Solution

Q5. If A = {4,5,6} , B = {4,6,7,8,9} and R is a relation from A and B defined by x is greater than y, then the Range is .

(a) {5,6} (b) {4} (c) {2} (d) {6}

Solution.
(b) {4}
Solution

Q6. Find the Range of the function
f(x) =
x - 4/ 3 - x


(a) R - {-1} (b) R (c) R{1} (d) None of these

Solution.
(a) R - {-1}

y =
x - 4/ 3 - x


x =
4 + 3y/ y + 1
Solution

Q7. If f : R → Rf(x) = e-x then f of (-1) =

Solution.
f(x) = e-x

f of (x) = f(f(x))

= f( e-x)

= ee-x

f of (-1) = ee-1 =e(-1/e)
Solution

Q8. Let f:R → R be such that f(x) = 2x, then f(x + y) equal :

Solution.
F(x+y) = e(x+y)

ex . ey = f(x) . f(y)
Solution

Q9. If f:R → R , f(x) = 2x + 7, then the inverse of f is :

Solution.
f-1 (x) = (x - 7)/2
Solution

Q10. On the set of lines , being perpendicular is a ______ relation .
(a) Transitive (b) Reflexive (c) Symmetric (d) None of these

Solution.
(c) Symmetric
Solution