**We know that**

range f = {1, 2, 3, 4} and domain (g) = {1, 2, 3, 4}

So range (f) ⊆ domain (g)

**(i) We know that domain (g o f) = domain (f) = {1, 2, 3, 4}**

**By substituting the values**

(g o f) (1) = g{f(1)} = g(4) = 4

(g o f) (2) = g{f(2)} = g(1) = 3

(g o f) (3) = g{f(3)} = g(3) = 2

(g o f) (4) = g{f(4)} = g(2) = 1

**Therefore, g o f = {(1, 4), (2, 3), (3, 2), (4, 1)}**

**(ii) We know that domain (f o g) = domain (g) = {1, 2, 3, 4}**

**By substituting the values**

(f o g) (1) = f{g(1)} = f(3) = 3

(f o g) (2) = f{g(2)} = f(1) = 4

(f o g) (3) = f{g(3)} = f(3) = 2

(f o g) (4) = f{g(4)} = f(4) = 2

**Therefore, f o g = {(1, 3), (2, 4), (3, 2), (4, 2)}**

**(iii) We know that domain (f o f) = domain (f) = {1, 2, 3, 4}**

**By substituting the values**

(f o f) (1) = f{f(1)} = f(4) = 2

(f o f) (2) = f{f(2)} = f(1) = 4

(f o f) (3) = f{f(3)} = f(3) = 4

(f o f) (4) = f{f(4)} = f(2) = 1

**Therefore, f o f = {(1, 2), (2, 4), (3, 3), (4, 1)}**