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`
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
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.