Let ƒ 1 : R → R, ƒ 2 : ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π − 2 , 2 → R, ƒ 3 : (–1, 2 e π – 2) → R and ƒ 4 : R → R be functions defined by (i) ƒ 1 (x) = sin( 2 x e 1 − − ), (ii) ƒ 2 (x) = ⎪ ⎩ ⎪ ⎨ ⎧ = ≠ − 0 x if 1 0 x if x tan | x sin | 1 , where the inverse trigonometric function tan –1 x assumes values in ⎟ ⎠

Question

Let ƒ 1 : R → R, ƒ 2 : ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π − 2 , 2 → R, ƒ 3 : (–1, 2 e π – 2) → R and ƒ 4 : R → R be functions defined by (i) ƒ 1 (x) = sin( 2 x e 1 − − ), (ii) ƒ 2 (x) = ⎪ ⎩ ⎪ ⎨ ⎧ = ≠ − 0 x if 1 0 x if x tan | x sin | 1 , where the inverse trigonometric function tan –1 x assumes values in ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π π − 2 , 2 (iii) ƒ 3 (x) = [sin (log e (x + 2))], where, for t ∈ R, [t] denotes the greatest integer less than or equal to t (iv) ƒ 4 (x) = ⎪ ⎩ ⎪ ⎨ ⎧ = ≠ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 0 x if 0 0 x if x 1 sin x 2 List-I List-II (P) The function ƒ 1 is (1) NOT continuous at x = 0 (Q) The function ƒ 2 is (2) continuous at x = 0 and NOT differentiable at x = 0 (R) The function ƒ 3 is (3) differentiable at x = 0 and its derivative is NOT continuous at x = 0 (S) The function ƒ 4 is (4) differentiable at x = 0 and its derivative is continuous at x = 0 The correct option is :

Accepted Answer

(P) → (2); (Q) → (1); (R) → (4); (S) → (3)

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