Question

Given that f(x)=x, g(x)=x-1:

h(x)=sqrt(x-1)

find f0g0h.

Answer 1

f(x)=x

g(x)=x-1
h(x)=√(x-1)
Since composition of functions is associative, i.e.
f ° (g ° h) = (f ° g) ° h,
the order of composition is not important.
(f°g°h)(x)
= f°(g(h(x)))
=f(g(h(x)))
=f(g(√(x-1)))
=f(√(x-1)-1)
=√(x-1)-1