Question Solution: (4) f (x) = x, when x is rational and 0 when x is irrational g (x) = 0, when x is rational and x when x is irrational... View Article
Solution: (3) f : X → Y X : domain and Y : codomain One-one function definition: x1 ≠ x2 f (x1) ≠f (x2) Onto function definition:... View Article
Solution: (2) f : R → R Domain = R Codomain = R f (x) = (x - 1) (x - 2) (x - 3) The coeffiecient of x3 is 1. f (x1) = f (x2) = f (x3) =... View Article
Solution: (4) Given that A = [-1, 1] and f : A → A is defined as f (x) = x|x|,∀ x ∈ A f (x) = x2 for x > 0 and f (x) = −x2 for x < 0 f... View Article
Solution: (4) f (x) = e2ix = cos 2x + i sin 2x The domain is R and the codomain is C. The periodic functions are not one-one, hence, the... View Article
Solution: (3) f (n) = 1 + n2 If n = 1, f (n) = 2 If n = 2, f (n) = 5 If n = 3, f (n) = 10 f (n) is one-one. As range ≠codomain, f (n)... View Article
Question Solution: (4) f (n) = n, n2 and 2n+1 is odd ∀ n ∈ N f (n) is not even. ⇒ It is not onto or not surjective. Since, f (3) =... View Article
Solution: (3) f (x) = x2 + x + 1 The discriminant D = 1 - 4 = -3 f ‘ (x) = 2x + 1 = 0 x = -1 / 2 The function is increasing. f (1) = 3, f... View Article
Solution: (4) f : C → R f (z) = |z| ∀ z ∈ C f (1) = |1| = 1 f (-1) = |-1| = 1 f (1) = f (-1) but 1 ≠ -1 Since there is an absence of... View Article
Solution: (4) Given that n (A) = 4 and n (B) = 6 n (B) > n (A) The function is one-one function. The number of one-one function mapping... View Article
Question: . Solution: (3) f (2) = {2 / 2 = 0, 1, 2, 3, 4, 5…} Every odd value of n yields zero. So, it is a many-one function. f (n) =... View Article
Solution: (3) f is one-one and onto R f (x) = x3 + 5x + 1 f '(x) = 3x2 + 5 > 0 ∀ x ∈ R. f(x) is strictly increasing on R⇒ f(x) is one-one... View Article
Solution: (3) At x = 1, f (x) = 3 At x = 2, f (x) = 4 At x = 3, f (x) = 5 At x = 4, f (x) = 6 f (x) is one-one but into since codomain ≠range.... View Article
