If g(k)=5, then what does kg(-k) equal?

Question

suppose k is a real constant and g(x) is an odd function. if g(k)=5, then kg(-k)=

This is for AP Calculus Review and I am a bit confused. It is multiple choice though

a.) -5k    b.) -k   c.) -5   d.) k    e.) 5k

The answer is supposed to be a.) but why?

Answer 1

g(k) is an odd function so g(-k)=-g(k).

If g(k)=5, g(-k)=-5, so kg(-k)=-5k, answer a.

For example, g(x)=10sin(x), g(-x)=-10sin(x).

If k=π/6, g(k)=5, g(-k)=-5, kg(-k)=-5π/6.