(i) g o f

To find: g o f

Formula used: g o f = g(f(x))

Given: (i) f : R → R : f(x) = (2x + 1)

(ii) g : R → R : g(x) = (x² - 2)

Solution: We have,

g o f = g(f(x)) = g(2x + 1) = [ (2x + 1)² – 2 ]

⇒ 4x² + 4x + 1 – 2

⇒ 4x² + 4x – 1

Ans). g o f (x) = 4x² + 4x – 1

(ii) f o g

To find: f o g

Formula used: f o g = f(g(x))

Given: (i) f : R → R : f(x) = (2x + 1)

(ii) g : R → R : g(x) = (x² - 2)

Solution: We have,

f o g = f(g(x)) = f(x² - 2) = [ 2(x² - 2) + 1 ]

⇒ 2x² - 4 + 1

⇒ 2x² – 3

Ans). f o g (x) = 2x² – 3

(iii) f o f

To find: f o f

Formula used: f o f = f(f(x))

Given: (i) f : R → R : f(x) = (2x + 1)

Solution: We have,

f o f = f(f(x)) = f(2x + 1) = [ 2(2x + 1) + 1 ]

⇒ 4x + 2 + 1

⇒ 4x + 3

Ans). f o f (x) = 4x+ 3

(iv) g o g

To find: g o g

Formula used: g o g = g(g(x))

Given: (i) g : R → R : g(x) = (x² - 2)

Solution: We have,

g o g = g(g(x)) = g(x² - 2) = [ (x² - 2)² – 2]

⇒ x⁴ -4x² + 4 - 2

⇒ x⁴ -4x² + 2

Ans). g o g (x) = x⁴ -4x² + 2