If f(x + f(x)) = x2 – 3x + 5 and f(1) = 2, then find f(34).
Explanation:
Given, f(x + f(x)) = x2 – 3x + 5 …(1)
putting x = 1, we get
f(1 + f(1)) = 12 – 3 × 1 + 5 = 3.
⇒ f(3) = 3
Now, substitute x = 3.
f(3 + f(3)) = 32– 3 × 3 + 5 = 5.
⇒ f(6) = 5
Now, substitute x = 6.
f(6 + f(6)) = 62– 3 × 6 + 5 = 23.
⇒ f(11) = 23.
Now, substitute x = 11.
f(11 + f(11)) = 112– 3 × 11 + 5 = 93.
⇒ f(34) = 93.
Hence, option (a).
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