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Determine whether the following function...

Determine whether the following functions are even or odd.
`{:((i)f(x)=log(x+sqrt(1+x^(2))),(ii)f(x)=x((a^(x)+1)/(a^(x)-1))),((iii)f(x)=sinx+cosx,(iv)f(x)=x^(2)-abs(x)),((v)f(x)=log((1-x)/(1+x)),(vi)f(x)={(sgn x)^(sgnx)}^(n)," n is an odd integer"):}`
`{:((vii) f(x)=sgn(x)+x^(2),""),((viii)f(x+y)+f(x-y)=2f(x)*f(y)," where " f(0) ne 0 and x","y ne R.,""):}`

Text Solution

Verified by Experts

The correct Answer is:
(i)odd (ii) even (iii) neither even nor odd (iv) even (v) odd (vi) odd (vii) neither even nor odd (viii) even
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Knowledge Check

  • If f(x-y),f(x)*f(y),f(x+y) are in for all x,y in R " and " f(0) ne 0 , then

    A
    f'(x) is an even function
    B
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    D
    f'(3)+f'(-3)=0

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