Is the function h(x) odd, even, or neither?

Question

This is the problem I'm stuggling on.#h(x)=(2x^2)/(5x^3)#

even formula y=f(-x)
odd formula y=-f(x)

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Answer 1 · 2017-10-04T06:31:51

It is an odd function. See explanation.

To check if the function #h(x)# is odd, even, or neither you have to calculate the value of #h(-x)# and compare it to the original function.

Here we have:

#h(-x)=(2(-x)^2)/(5(-x)^3)=(2x^2)/(-5x^3)=-(2x^2)/(5x^3)=-h(x)#

We calculated, that #h(-x)=-h(x)#, this is the condition of the odd function, so #h(x)# is odd.