Answer :

True

In order to prove composition of functions is associative we need to show


[fo(goh)](x) = [(fog)oh](x)


Let us suppose, f(x) = x, g(x) = 2x, h(x) = x + 2


Now,


[fo(goh)](x) = f(g(h(x))) = f(g(x+2)) [ h(x) = x + 2 ]


= f(2(x+2)) = f(2x+4)


= 2x+4 (i)


[(fog)oh](x) = (fog)oh(x) = (fog)(h(x))


= (fog)(x+2) = f(g(x+2))


= f(2(x+2)) = f(2x+4)


= 2x+4 (ii)


From (i) and (ii), we observe that


[fo(goh)](x) = [(fog)oh](x)


Thus, composition of functions is associative.


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