Question

f (x) = ax + b and g (x)= x-4,where a and b are constant .If fg (4) = 2 and gf(2)=4,find the values of a and b.

Answer 1

Answer: a = 3, b = 2

Explanation:

f(x) = ax + b f(2) = 2a + b

g(x) = x - 4 g(4) = 4 - 4 ⇒ g(4) = 0

f(g(4)) = 2 ⇒ f(0) = 2

and f(0) = a(0) + b ⇒ f(0) = b

⇒ 2 = b

g(f(2)) = 4 ⇒ g(2a+b) = 4

and g(2a + b) = (2a + b) - 4 ⇒ g(2a + 2) = 2a + 2 - 4 ⇒ g(2a + 2) = 2a - 2

⇒ 4 = 2a - 2

6 = 2a

3 = a