Question

if f(x) = x^3 on [-2,1], is f odd?

Answer 1

yes

Answer 2

how so ?

Answer 3

Take any -x with x from [-2,1] and test f(-x)

Answer 4

ok, take x = -2 f(-(-2)) = ??

Answer 5

Normally we work it with a variable to prove it for all x in the given domain.
Like for x in [-2,1], f(-x)=(-x)^3=-x^3=-f(x)
So f is odd on [-2,1].

Answer 6

so you're saying f(-(-2)) = -f(-2)? But 2 isn't in the domain

Answer 7

What exactly are trying to prove ?

Answer 8

if f is odd or not

Answer 9

So why do you go for specific values, you just need to prove it for that in the domain given.
Fyi x^3 is odd for all real numbers i.e on \([-\infty,+\infty]\) ;]

Answer 10

oh ok. Thanks :)

Answer 11

Welcome =)