- #1

dyn

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I would like to check that my understanding is correct. For ##f(x)=x^{1/n}## where n is an integer. If n is odd then f(x) is an odd function while if n is even then f(x) is neither odd or even as it involves the square root function which is only defined for non-negative x.

For ## f(x) = x^{m/n}## where n and m are integers then the above rule applies and if m is even then f(x) is even and m odd gives f(x) odd.

Examples ## f(x) = x^{1/4} ## and ## f(x) = x^{3/2}## are neither odd or even as they are only defined for non-negative x and ##f(x) = x^{2/5}## is even and ##f(x) = x^{3/5}## is odd.

Have i got all this right ?

Thanks