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If f (2x + 3y, 2x – 7y) = 20x, then f(x, y) equals

(a) 7x - 3y (b) 7x + 3y (c) 3x - 7y (d) 3x + 7y Solution: Given f(2x + 3y, 2x - 7y) = 20x Let 2x + 3y = X ..(i) 2x - 7y... View Article

Let f(x) = αx²/(x+1), x ≠ -1. The value of α for which f(a) = a, (a ≠ 0) is

(a) 1 - (1/a) (b) 1/a (c) 1 + (1/a) (d) (1/a) - 1 Solution: f(x) = αx2/(x+1) f(a) = a => αa2/(a+1) = a =>... View Article

If f (x) = e^-x, then f(-a)/f(b) is equal to

(a) f (a + b) (b) f (a - b) (c) f (- a + b) (d) f (- a - b) Solution: Given f(x) = e-x f(-a) = ea f(b) = e-b... View Article

The function f(x) = log(x + √(x²+1)), is

(a) neither an even nor an odd function (b) an even function (c) an odd function (d) a periodic function Solution: Given f(x) = log(x +... View Article

Let f (x) = x, g(x) = 1/x and h(x) = f(x) g(x). Then, h(x) = 1 if and only if

(a) x is a real number (b) x is a rational number (c) x is an irrational number (d) x is a non-zero real number Solution: Given f(x) =... 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

The domain of the function f(x) = √(x¹⁴ – x¹¹ + x⁶ – x³ + x² + 1) is

(a) (-∞,∞) (b) [0,∞) (c) (- ∞,0] (d) R \ [0,1] Solution: f(x) = √(x14 - x11 + x6 - x3 + x2 +... View Article

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

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