A function f is defined by f(x) = x + 1/x. Consider the following. (1) (f(x))2 = f(x2) + 2 (2) (f(x))3 = f(x3) + 3f(x) Which of the above is/are correct? (a) 1 only (b) 2 only (c) Both 1 and... View Article
If f(x + 1) = x2 – 3x + 2, then f (x) is equal to: (a) x2 - 5x - 6 (b) x2 + 5x – 6 (c) x2 + 5x + 6 (d) x2 - 5x + 6 Solution: Given f(x + 1) = x2 - 3x + 2. This... View Article
If f(x) = (2x + 2-x)/2, then f(x+y).f(x-y) is equal to (a) ½ [f(x+y) + f(x-y)] (b) ½ [f(2x) + f(2y)] (c) ½ [f(x+y). f(x-y)] (d) none of these Solution: Given f(x) = (2x... View Article
If 3f(x) – f (1/x) = log x4, then f(e-x) is (a) 1+ x (b) 1/x (c) x (d) - x Solution: Use log mx = x log m Given 3f(x) - f (1/x) = log x4 => 3f(x) - f... View Article
Let f be a function on R given by f (x) = x2 and let E = {x∈ R: -1 ≤ x ≤ 0} and F = {x∈ R: 0 ≤ x ≤ 1} then which of the following is false? (a) f(E) = f(F) (b) E â‹‚ F ⊂ f(E) â‹‚ f(F) (c) E ⋃ F ⊂ f(E) ⋃ f(F) (d) f (E â‹‚ F) = {0} Solution: Given f (x) = x2 E = {x∈... View Article
The domain of the function f(x) = log2( – log1/2 (1 + 1/x1/4) – 1) is (a) (0, 1) (b) (0, 1] (c) [1, ∞) (d) (1, ∞) Solution: Given f(x) = log2( - log1/2 (1 + 1/x1/4) - 1) f(x) is defined... View Article
The domain of the function f(x) = √(x- √(1 – x2)) is (a) [-1, -1/√2] ⋃ [1/√2, 1] (b) [-1,1] (c) (-∞, -½] ⋃ [1/√2, ∞) (d) [1/√2, 1] Solution:... View Article
The domain of f(x) = (1/√(2x-1)) – √(1-x2) is (a) ]½, 1[ (b) [-1, ∞[ (c) [1, ∞[ (d) none of these Solution: Given f(x) = (1/√(2x-1)) - √(1-x2) = p(x)... View Article
Find the domain of the function f(x) = √[(2/(x2-x+1)) – 1/(x+1) – (2x-1)/(x3+1))]. (a) (-∞, 2] - {-1} (b) (-∞, 2) (c) ] -1, 2] (d) None of these Solution: Given f(x) = √[(2/(x2-x+1)) -... View Article
Which of the following relation is NOT a function? (a) f = {(x, x) | x ∈ R} (b) g = {(x, 3) | x ∈ R} (c) h = {(n,1/n)| n∈ I} (d) t = {(n, n2) | n ∈ N} Solution:... View Article
The domain of the function √(x2 -5x+6) + √(2x+8-x2) is (a) [2, 3] (b) [-2, 4] (c) [-2, 2] ⋃ [3, 4] (d) [-2, 1] ⋃ [2, 4] Solution: Given f(x) = √(x2 -5x+6) +... View Article
Let A = {x ∈ W, the set of whole numbers and x < 3}, B = {x∈ N, the set of natural numbers and 2 ≤ x < 4} and C = {3, 4}, then how many elements will (A⋃B)×C contain? (a) 6 (b) 8 (c) 10 (d) 12 Solution: Given A = {x ∈ W, the set of whole numbers and x < 3}. B = {x∈ N,... View Article
Suppose that the number of elements in set A is p, the number of elements in set B is q and the number of elements in A × B is 7. Then p2 + q2 = (a) 42 (b) 49 (c) 50 (d) 51 Solution: Given that number of elements in set A is p and the number of elements in set B... View Article
Let R = {x | x∈ N, x is a multiple of 3 and x ≤100}, S = {x | x ∈ N, x is a multiple of 5 and x ≤ 100}. What is the number of elements in (R × S) â‹‚ (S × R)? (a) 36 (b) 33 (c) 20 (d) 6 Solution: Given R = {x | x∈ N, x is a multiple of 3 and x ≤100} S = {x | x... View Article
Let A = {1, 2}, B = {3, 4}. Then, number of subsets of A × B is (a) 4 (b) 8 (c) 18 (d) 16 Solution: Given A = {1, 2}, B = {3, 4} A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}... View Article
If A = {a, b, c, d}, B = {1, 2, 3}, which of the following sets of ordered pairs are not relations from A to B? (a) {(a, 1), (a, 3)} (b) {(b, 1), (c, 2), (d, 1)} (c) {(a, 2), (b, 3), (3, b)} (d) {(a, 1), (b, 2), (c, 3)} Solution: {(a, 1), (a, 3)}... View Article
If A = {1, 2}, B = {1, 3}, then (A × B) ⋃ (B × A) is equal to (a) {(1, 3), (2, 3), (3, 1), (3, 2), (1, 1), (2, 1), (1, 2)} (b) {(1, 3), (3, 1), (3, 2), (2, 3)} (c) {(1, 3), (2, 3), (3, 1), (3, 2), (1,... View Article
The domain and range of the relation R given by R = {(x, y) : y = x + 6/x, where x, y ∈ N and x < 6} is (a) {1, 2, 3}, {7, 5} (b) {1, 2}, {7, 5} (c) {2, 3}, {5} (d) None of these Solution: Given R = {(x, y) : y = x + 6/x: x, y... View Article
A relation R is defined over the set of non-negative integers as xRy => x2+y2=36. What is R? (a) {(0, 6)} (b) {(6,0) (√11, 5), (3, 3√3) (c) {(6, 0), (0, 6)} (d) (√11, 5), (2, 4√2), (5 ,√11), (4√2,... View Article
The Cartesian product of two sets P and Q, i.e.,P × Q = Ø, if (a) either P or Q is the null set (b) neither P nor Q is the null set (c) Both (a) and (b) (d) None of these Solution: The Cartesian... View Article
