Odd and even function

[Gabriellaeid]

Would love if someone could please help me prove that if f(x) is an even function therefore -f(x) is also an even function

 

[Steven G]

We are given that f(x) = f(-x) since f is even.
Then -f(x) = -f(-x). Hence -f(x) is even

 

[apple2357]

That's a rigorous proof above but thinking about it graphically...

An even function has line symmetry about the y axis (e.g. y=x^2) , -f(x) has the effect of reflecting f(x) in the x axis. So -f(x) would still retain line symmetry ( about the y axis) and therefore would still be even.
I hope that makes sense!?