f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is (a) one-one (b) one-one onto (c) onto (d) many one What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4} (a) Reflexive (b) Transitive (c) Symmetric (d) None of these If F : R → R such that f(x) = 5x + 4 then which of the following is equal to f-1(x). (a) x−54 (b) x−y5 (c) x−45 (d) x4 -5 If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is (a) 12 (b) 28 (c) 61 (d) None of Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals (a) 31 (b) 40 (c) 43 (d) None of these The range of the function f(x) = (x−1)(3−x)−−−−−−−−−−−√ is (a) [1, 3] (b) [0, 1] (c) [-2, 2] (d) None of these If f: R → R defined by f(x) = 2x + 3 then f-1(x) = (a) 2x – 3 (b) x−32 (c) x+32 (d) None of these If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then (a) A = B (b) A = C (c) B = C (d) A ∩ B = d Let A = {1, 2}, how many binary operations can be defined on this set? (a) 8 (b) 10 (c) 16 (d) 20
If A = (1, 2, 3}, B = {6, 7, 8} is a function such that f(x) = x + 5 then what type of a function is f? (a) Many-one onto (b) Constant function (c) one-one onto (d) into
Let function R → R is defined as f(x) = 2x³ – 1, then ‘f’ is (a) 2x³ + 1 (b) (2x)³ + 1 (c) (1 – 2x)³ (d) (1+x2)1/3