Can anyone point me in the right direction on how to solve this? Prove there exists an alpha,beta,gamma of (0,1) with alpha

Question

Can anyone point me in the right direction on how to solve this? Prove there exists an alpha,beta,gamma of (0,1) with alpha<beta<gamma such that f(alpha)f(beta)f(gamma)=1 ? lso f is monotonic and continuous on [1,0] where the integral from 0 to 1 of f(t) dt =1

anonymous · Answer

I think this has something to do with the intermediate value theorum but I'm not positive