Archives

If f(x) = 1/√(x+1)(e^x – 1)(x-4)(x+5)(x-6), then the domain of f(x) is

(a) (-∞, -5) ⋃ (-1, 4) ⋃ (6, ∞) (b) (-∞, -5) ⋃ (-1, 0) ⋃ (0, 4) ⋃ (6, ∞) (c) (-5, -1) ⋃ (0, 4) ⋃ (6, ∞) (d)... View Article

The domain of the function f(x) = log_3+x(x² – 1) is

(a) (-3, -1) ⋃ (1, ∞) (b) [-3, -1) ⋃ [1, ∞) (c) (-3, -2) ⋃ (-2, -1) ⋃ (1, ∞) (d) [-3, -2) ⋃ (-2, -1) ⋃ [1, ∞)... View Article

If log_1/2(x² – 5x + 7) > 0, then exhaustive range of values of x is

(a) (-∞, 2)⋃ (3, ∞) (b) (2, 3) (c) (-∞, 1)⋃ (1, 2)⋃ (2, ∞) (d) None of these Solution: f(x) = log1/2 (x2 - 5x +... View Article

The domain of F(x) = log₂ (x+3)/(x² + 3x + 2) is

(a) R - {- 1, - 2} (b) (- 2, ∞) (c) R - {- 1, - 2 - 3} (d) (- 3 , ∞) - {-1, -2} Solution: F(x) = log2 (x+3)/(x2 + 3x... View Article

The domain and range of the function f given by f(x) = 2 – |x – 5| is

(a) Domain = R+, Range = (-∞, 1] (b) Domain = R, Range = (-∞, 2] (c) Domain = R, Range = (-∞, 2) (d) Domain = R+, Range =... View Article

The domain of the function f(x) = |x+3|/(x+3) is

The domain of the function f(x) = |x+3|/(x+3) is (a) {-3} (b) R - {-3} (c) R - {3} (d) R Solution: Given f(x) = |x+3|/(x+3) For f(x) to be... View Article

The domain for which the functions f(x) = 2x² – 1 and g(x) = 1 – 3x is equal, i.e. f(x) = g(x), is

(a) {0, 2} (b) {1/2, -2} (c) {-½, 2} (d) {1/2, 2} Solution: Given f(x) = 2x2 - 1 g(x) = 1 - 3x f(x) = g(x) => 2x2 - 1 =... View Article

Domain of the function f(x) = 3/(4-x²) + log₁₀ (x³-x) is

(a) (1, 2) (b) (-1, 0) ∪ (1, 2) (c) (1, 2) ∪ (2, ∞) (d) (-1, 0) ∪ (1, 2) ∪ (2, ∞) Solution:... View Article

Consider the following statements.

Consider the following statements. 1. If (a, 1), (b, 2) and (c, 1) are in A × B and n(A) = 3, n (B) = 2, then A = {a, b, c} and B = {1,... View Article

Consider the following statements. Let A = {1, 2, 3, 4} and B = {5, 7, 9}

Consider the following statements. Let A = {1, 2, 3, 4} and B = {5, 7, 9} 1. A × B = B × A 2. n (A × B) = n (B × A)... View Article

f(x) = [x(x-p)/(q-p)] + [x(x-q)/(p-q)], p≠q. What is the value of f(p) + f(q)?

(a) f(p-q) (b) f(p+q) (c) f(p(p+q)) (d) f(q(p-q)) Solution: f(x) = [x(x-p)/(q-p)] + [x(x-q)/(p-q)] = [-x(x-p)/(p-q)] + [x(x-q)/(p-q)]... View Article

If f : R→ R and g: R→ R be two given functions, then 2 min {f (x) – g(x), 0} equals

If f : R → R is defined by f(x) = 3x + |x| , then f(2x) – f(-x) – 6x =

(a) f(x) (b) 2f(x) (c) - f(x) (d) f (-x) Solution: Given that f(x) = 3x + |x| f(2x) = 6x + 2|x| f(-x) = -3x... View Article

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) = (2^x + 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 ⋂ F ⊂ f(E) ⋂ f(F) (c) E ⋃ F ⊂ f(E) ⋃ f(F) (d) f (E ⋂ F) = {0} Solution: Given f (x) = x2 E = {x∈... View Article

The domain of the function f(x) = log₂( – log_1/2 (1 + 1/x^1/4) – 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

M	T	W	T	F	S	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30
31