If the function f(x)= cases [a(x+1)+ x] 2 x , & x 0 cases is continuous at x=0 , then which of the option(s) can be true (not necessary simultaneously)? [Note: [k] denotes greatest integer function less than or equal to k .]

Question

Quantrex Academy · Accepted Answer

Correct answer: D. f(1)=1 / 3

L.H.L. = _ x 0⁻ [a(x+1)]+ x 2 x for limit exist a [0,1)= _ x 0⁻ x+0 2 x = 1 2 R.H.L. = _ x 0⁺ (1+b x)^ 1 / 2 -1 b x = _ x 0⁺ (1+ b x 2 + )-1 b x = 1 2 b R- 0 c= 1 2 ; a [0,1) So, b R- 0 f(1)= b+1 -1 b = 1 b+1 +1 = 1 3 b=3

If the function f(x)= cases [a(x+1)+ x] 2 x , & x 0 cases is continuous at x=0 , then which of the option(s) can be true (not necessary simultaneously)? [Note: [k] denotes greatest integer function less than or equal to k .]

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Correct answer

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