Let f : R → R : f(x) = (x2 + 3x + 1) and g: R → R : g(x) = (2x - 3). Write down the formulae for
(i) g o f
(ii) f o g
(iii) g o g
(i) g o f
To find: g o f
Formula used: g o f = g(f(x))
Given: (i) f : R → R : f(x) = (x2 + 3x + 1)
(ii) g: R → R : g(x) = (2x - 3)
Solution: We have,
g o f = g(f(x)) = g(x2 + 3x + 1) = [ 2(x2 + 3x + 1) – 3 ]
⇒ 2x2 + 6x + 2 – 3
⇒ 2x2 + 6x – 1
Ans). g o f (x) = 2x2 + 6x – 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) = (x2 + 3x + 1)
(ii) g: R → R : g(x) = (2x - 3)
Solution: We have,
f o g = f(g(x)) = f(2x - 3) = [ (2x - 3)2 + 3(2x – 3) + 1 ]
⇒ 4x2 - 12x + 9 + 6x – 9 + 1
⇒ 4x2 - 6x + 1
Ans). f o g (x) = 4x2 - 6x + 1
(iii) g o g
To find: g o g
Formula used: g o g = g(g(x))
Given: (i) g: R → R : g(x) = (2x - 3)
Solution: We have,
g o g = g(g(x)) = g(2x - 3) = [ 2(2x – 3) - 3 ]
⇒ 4x – 6 - 3
⇒ 4x - 9
Ans). g o g (x) = 4x – 9