Let f : R  R and g : R  R be functions defined by f(x) =              , 0 x , 0 , 0 x , x 1 sin | x | x and g(x) =         , otherwise , 0 , 2 1 x 0 , x 2 1 Let a, b, c, d  R. Define the function h : R  R by h(x) = af(x) + b                 x 2 1 g

Question

Let f : R  R and g : R  R be functions defined by f(x) =              , 0 x , 0 , 0 x , x 1 sin | x | x and g(x) =         , otherwise , 0 , 2 1 x 0 , x 2 1 Let a, b, c, d  R. Define the function h : R  R by h(x) = af(x) + b                 x 2 1 g ) x ( g + c(x – g(x)) + d g(x), x  R, Match each entry in List-I to the correct entry in List-II . List-I List-II (P) If a = 0, b = 1, c = 0, and d = 0, then (1) h is one-one (Q) If a = 1, b = 0, c = 0, and d = 0, then (2) h is onto (R) If a = 0, b = 0, c = 1, and d = 0, then (3) h is differentiable on R (S) If a = 0, b = 0, c = 0, and d = 1, then (4) the range of h is [0, 1] (5) the range of h is {0, 1} The correct option is

Accepted Answer

(P)  (5), (Q)  (3), (R)  (2), (S)  (4)

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