Question

Given two functions f(x) = ax + b , g(x) = 1-x + x2 and (g º f)(x) = 9x2 – 9x + 3 . Find the values a and b.

Answer 1

Answer:

a=+3 or -3

b=-1 or +2

Step-by-step explanation:

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Answer 2

answer : a = 3 and b = -1 or a = -3 and b = 2

Given, two functions f(x) = ax + b, g(x) = 1 - x + x²

and (g o f)(x) = 9x² - 9x + 3

we know, (g o f)(x) = g(f(x))

⇒9x² - 9x + 3 = g(ax + b)

⇒9x² - 9x + 3 = 1 - (ax + b) + (ax + b)²

⇒9x² - 9x + 3 = 1 - ax - b + a²x² + 2abx + b²

⇒9x² - 9x + 3 = a²x² + (2ab - a)x + (b² - b + 1)

on comparing we get,

a² = 9 ⇒a = ±3

and 2ab - a = -9

case 1 : when a = 3

⇒2(3)b - 3 = -9

⇒6b = -6

⇒b = -1

case 2 : when a = -3

2(-3)b -(-3) = -9

⇒-6b =-12

⇒b = 2