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 –... View Article
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If f(x) = 1/√(x+1)(ex – 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,... View Article
The domain of the function f(x) = log3+x (x2 – 1) is
(a) (-3, -1) ⋃ (1, ∞) (b) [-3, -1) ⋃ [1, ∞) (c) (-3, -2) ⋃ (-2, -1) ⋃ (1,... View Article
If log1/2 (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:... 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} ... 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,... 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)... 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)... 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,... 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)... 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 ×... 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)] = (-x2... View Article
If f : R→ R and g: R→ R be two given functions, then 2 min {f (x) – g(x), 0} equals
(a) f (x) + g(x) – |g(x) – f (x)| (b) f (x) + g(x) + |g(x) – f (x)|... View Article
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) =... 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... 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... 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... 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)... 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)... 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... View Article
