Solution: The number of subsets of A consisting of m elements is 112 > the subsets of B having n elements. 2m − nn = 112 2n . (2m−n − 1)... View Article
Solution: (1) bN = {bx/x ∈ N} = the set that consists of +ve integer multiples of b cN = {cx/x ∈ N} = the set that consists of +ve integer... View Article
Let g (x) = 1 + x - [x] and f (x) =. Then for all x, f (g (x)) is equal to 1) x 2) 1 3) f (x) 4) g (x) Solution: (2) g (x) = 1 + x - [x]... View Article
Solution: (3) Putting y = x, 2f (x) = f (2x √1 - y2) Take x = sin θ, 2 f (sin θ) = f (2 sin θ) Putting x = sin θ and y = sin 2θ in the given... View Article
Solution: (2) Let y = f (x) = [x - [x]] / [1 + x - [x]], x ∈ R If x ∈ I, then f (x) = 0 Again for any x ∈ R - I, x - [x] < 1 Hence 2 (x... View Article
Solution: (3) Since f (g (x)) = x (fog) (x) = x fog = 1 g (x) = f-1 (x) Now y = f (x) = [ex - e-x] / 2 2y = ex - [1 / ex] = [e2x - 1] /... View Article
1) f (x) = sin2 x and g (x) = √x 2) f (x) = sinx and g (x) = [x] 3) f (x) = x2 and g (x) = sin √x 4) f and g cannot be determined Solution:... View Article
Solution: Given a2-2a sin x+1 = 0 This is a quadratic equation in a. So a = [2 sin x±√(4 sin2x-4)]/2 = [2 sin x ±2√-(1- sin2x)]/2 = sin x... View Article
