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If F X X 1 X 1 12 Then D F Is

1) R –{–1, 1} 2) [0, 1) 3) (– ∞, −1] ∪ [0, 1) 4) None of these Solution: (2)... View Article

1) ( − ∞, 4] 2) [3, ∞) 3) ( –∞, 1] ∪ [3, 4] ∪ [4. 5, ∞) 4)... View Article

1) {-1, 0, 1} 2) {nπ : n ∈ I} 3) {nπ / 3 : n ∈ I} 4) None... View Article

Solution: (3) √x2 – [x2] > 0 x2 – [x]2 > 0 x ∈ I [x] = x x2 ∈... View Article

Solution: (4) f (x + [1 / x]) = x2 + (1 / x2) + 2 – 2 = x2... View Article

Solution: (1) f (x) = (1 / [1 – x]) g (x) = f (f (x)) h (x) = f... View Article

Solution: (2) f (x) = [(x / √1 + x2)] [f (x)]2 = [(x2 / 1 + x2)] (fof) (x)... View Article

Solution: (4) f (x) = sin (π / x) [As f (x) > 0] = [x : (π / x)... View Article

Solution: (2) f (x) = λ |sinx| + λ2 |cosx| + g (λ) f (x) is a periodic function with... View Article

Solution: (4) y = loga (x + √x2 + 1) Let f (x) = y x = f-1 (y) (x... View Article

Solution: f (x) = cos-1 (x – x2) + √(1 – [1 / |x|]) + 1 / [x2 – 1]... View Article

Solution: (4) y = f (x) = log10 log10 log10…log10 x (n times) log10 log10 log10…log10 x > 0 log10... View Article

Solution: (2) f (x) = (1 / 2) ([|sinx| / cosx] + [sinx / |cosx|] f (2π + x) =... View Article

Solution: (1) (fog)-1 (x) = (g-1 o f-1) (x) Since, f (x) = x + 1 ,y = x +... View Article

Solution: (1) -1 ≤ [(2 – |x|) / 4] ≤ 1 -∞ ≤ [2 – 1 * 1] / 4 ≤ ... View Article

Solution: (3) f (x) = 1 / √([x]2 – 2 [x] – 8) [x]2 – 2 [x] – 8 >... View Article

Solution: (4) f (x) = 6x + 6|x| f (x) ≥ 2 Range = [2, ∞) It is a many one... View Article

Solution: (2) f (x) = 3 sin (πx / 3) + 4 cos (πx / 4) Period of f (x)... View Article

Solution: (3) Since -1 < sin θ ≤ 1 ∀ θ ∈ R Rf = [-1, 1]

Solution: (3) f (x) = x2 and g (x) = 2x f (g (x)) = g (f (x)) f (2x)... View Article