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Question
A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f(x))2
Solution
f(x) = 3 – 2x
f(x2) = 3 – 2 (x2)
= 3 – 2x2
(f(x))2 = (3 – 2x)2
= 9 + 4x2 – 12x
But f(x2) = (f(x))2
3 – 2x2 = 9 + 4x2 – 12x
–2x2 – 4x2 + 12x + 3 – 9 = 0
–6x2 + 12x – 6 = 0
(÷ by – 6) ⇒ x2 – 2x + 1 = 0
(x – 1) (x – 1) = 0
x – 1 = 0 or x – 1 = 0
x = 1
The value of x = 1
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