Question

f : R—>R, g : R—>R, h : R—>R are functions. Prove: (fog)oh= fo(goh)

Answer 1

we have to prove : (fog)oh = for(goh)

proof :- it is based on theory of composite function. if we write fog means f(g(x))
now, LHS = (fog)oh
= f(g(x))oh
= f{g(h(x))}
= f{goh(x)}
= fo(goh) = RHS
hence, proved

for example :- Let's take three function f, g , h in such a way that f : R ---> R , g: R ---->R and h:R ---->R
Let f(x) = x, g(x) = x³ and h(x) = 1 + x

now, f(g(x)) = x³ => (fog)oh = (1 + x)³
g(h(x)) = (1 + x)³=> fo(goh) = (1 + x)³

hence, (fog)oh = fo(goh)