Answer :

Given that, f (x) = x2 + 3x + 1, g (x) = 2x – 3


(i) f o g


fog = f(g(x)) = f(2x-3)


= (2x-3)2 + 3(2x-3) + 1


= (4x2-12x+9) + 6x – 9 +1


= 4x2 - 6x + 1


fog = 4x2 - 6x + 1


(ii) g o f


gof = g(f(x)) = g(x2 + 3x + 1)


= 2(x2 + 3x + 1) – 3


= 2x2 + 6x + 2 – 3


= 2x2 + 6x – 1


gof = 2x2 + 6x – 1


(iii) f o f


fof = f(f(x)) = f(x2 + 3x + 1)


= (x2 + 3x + 1)2 + 3(x2 + 3x + 1) + 1


= x4+9x2+1+6x3+6x+2x2+3x2+9x+3+1


= x4+6x3+14x2+15x+5


fof = x4+6x3+14x2+15x+5


(iv) g o g


gog = g(g(x)) = g(2x-3)


= 2(2x-3) – 3


= 4x-6-3


= 4x-9


gog = 4x-9


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