Is it necessary that fo(g+h) is always equal to (fog) + (foh)? Explain using an example.

No.

Let us consider f(x) = x2 , g(x) = 3 and h(x) = 1.

Then fo(g+h) = f(3+1) = f(4) = 42 = 16.

But (fog) + (foh) = f(3) + f(1) = 32 + 12 = 10.

Hence fo(g+h) is not necessarily equal to fog + foh.

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