InterviewSolution
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InterviewSolution
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Q. f={`(x+a if x=0)` `g(x)={(x+1 if x |
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Answer» Correct Answer - `g{f(x)}={{:(x+a+1", if "xlt -a),((x+a-1)^(2)", if "ale x lt c),(x^(2) +b", if "0le xle 1),((x-2)^(2)+b", if "xgt1):}` a=1, b = 0 gof is differentiable at x = 0 gof `(x) = {{:(f(x) +1", if " f(x) lt 0),({f(x)-1}^(2)+b", if " f(x) ge 0):}` ` ={{:(x+a+1", if " x lt -a),((x+a-1)^(2)+b", if " -a le x lt 0),((|x-1|-1)^(2)+b", if " c ge 0):}` As gof (x) is continuous at x =- a gof `(-a) = "gof "(-a^(+)) = " gof " (-a^(-)) ` `rArr" " 1+b = 1 + b = 1 rArr b = 0 ` Also, gof (x) is continuous at x = 0 `rArr" " "gof " (0) =" gof " (0^(+)) = " gof " (0^(-))` ` rArr" " b = b = (a-1)^(2) + b rArr a = 1` `"Hence, "gof(x) = {{:(x+2", if " x lt -1),(x^(2)", if " x lt -1),((|x-1|-1)^(2)", if " x ge 0):}` In the neighbourhood of x = 0, gof `(x) = x^(2)`, which is differentiable at x = 0. |
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