InterviewSolution
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InterviewSolution
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Let the function `f(x)=x^2+x+s in x-cosx+log(1+|x|)`be defined on the interval `[0,1]`.Define functions `g(x)a n dh(x)in[-1,0]`satisfying `g(-x)=-f(x)a n dh(-x)=f(x)AAx in [0,1]dot` |
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Answer» Correct Answer - `g(x)= -x^(2)+x+sinx +cosx -log(1+|x|)` `h(x)=x^(2)-x-sinx-cosx+log(1+|x|)` Clearly `g(x)` is the odd extension of the function `f(x)` and `h(x)` is the even extension. Since `x^(2),cosx, log(1+|x|)` are even functions and `x, sin x` and odd functions. `g(x)= -x^(2)+x+sinx +cosx-log(1+|x|)` and `h(x)=x^(2)-x-sinx-cosx +log(1+|x|)` Clearly this function satisfies the restriction of the problem. |
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