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functions

I have no idea how to do this question:

if f(x) is a nonzero function of x and g(x) is an odd function of x, determine whether:
i. f(x)-g(x) is odd, even or neither
ii. f(x) * g(x) is odd, even or neither
iii. [g(x)]^2/3 is odd, even or neither

I'd appreciate any help! Thanks
(edited 9 years ago)
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Avatar for TeeEm
TeeEm
19
Original post by HelloGoodbye
I have no idea how to do this question:

if f(x) is a nonzero function of x and g(x) is an odd function of x, determine whether f(x)-g(x)

I'd appreciate any help! Thanks


???
Original post by TeeEm
???


oops forgot to give the rest of the question!
Reply 3
Avatar for davros
davros
16
Original post by HelloGoodbye
I have no idea how to do this question:

if f(x) is a nonzero function of x and g(x) is an odd function of x, determine whether:
i. f(x)-g(x) is odd, even or neither
ii. f(x) * g(x) is odd, even or neither
iii. [g(x)]^2/3 is odd, even or neither

I'd appreciate any help! Thanks


Well for (i) and (ii), just choose a few random functions f(x) and see if you can deduce anything.

For (iii), write down what it means for g(x) to be an odd function, and see if you can deduce anything when you put -x into the composite function they've given you.

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