It is given that

f(x) = (x^{2} + 3x + 1) and g(x) = (2x – 3)

**(i) g o f = g o f (x) = g{f(x)} = g(x**^{2} + 3x + 1)

So we get

= 2 (x^{2} + 3x + 1) – 3

It can be written as

= 2x^{2} + 6x + 2 – 3

**On further calculation**

= 2x^{2} + 6x – 1

**(ii) f o g = f o g (x) = f{g(x)} = f {2x – 3}**

So we get

= (2x – 3)^{2} + 3 (2x – 3) + 1

It can be written as

= 4x^{2} – 12x + 9 + 6x – 9 + 1

On further calculation

= 4x^{2} – 6x + 1

**(iii) g o g = g o g (x) = g {g(x)} = g{2x – 3}**

So we get

= 2 (2x – 3) – 3

It can be written as

= 4x – 6 – 3

**On further calculation**

= 4x – 9