If f and g are functions defined for all real numbers, and f is an odd function,

Question

then f ∘ g is also an odd function. Justify.

I wrote false cause for example if f = x^3(odd) and g=x^2(even) the fog is even.

Answer 1

you are correct.

as an even simpler example, let

g(x) = x-1 (neither even nor odd)
f(x) = x (odd)

f∘g = x-1

Answer 2

Cheers Steve.