**It is given that**

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

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

So we get

= (2x + 1)^{2} – 2

It can be written as

= 4x^{2} + 4x + 1 – 2

On further calculation

= 4x^{2} + 4x – 1

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

So we get

= 2 {x^{2} – 2} + 1

It can be written as

= 2x^{2} – 4 + 1

**On further calculation**

= (2x^{2} – 3)

**(iii) f o f = f o f (x) = f{f(x)} = f(2x + 1)**

So we get

= 2 (2x + 1) + 1

It can be written as

= 4x + 2 + 1

**On further calculation**

= 4x + 3

**(iv) g o g = g o g (x) = g{g(x)} = g { x**^{2} – 2}

So we get

= (x^{2} – 2)^{2} – 2

**On further calculation**

= x^{4} – 4x^{2} + 4 – 2

We get

= x^{4} – 4x^{2} + 2