Engineering
Mathematics
Composition of Functions
Question
If f : R → R be a polynomial function such that f(f(x)) = 6 f (x) – 9x, then find the value of f(3).
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Solution
let degree of f(x) = n, n2 = n
⇒ n = 1 ⇒ f(x) = ax + b
a(ax + b) +b = 6(ax + b) – 9x
a2x + ab + b = (6a – 9)x + 6b
a2 = 6a – 9, ab + b = 6b
(a – 3)2 = 0, b(a – 5) = 0
a = 3, b = 0
⇒ f(x) = 3x
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