express the function in the form f o g. Use non identity functions for f and g

Question

express the function in the form f o g. Use non identity functions for f and g.

u(t)=cot(t)/7+cot(t)

f(t), g(t)= ?

Answer 1

Let g(t) = cot(t)   f(t) = t/(7+t)

 

Then (f º g)(t) = f(g(t)) = f(cot(t)) = cot(t)/[7 + cot(t)] = u(t)