if-f-x-x-2-2x-find-x-f-f-f-x-2-99-999-999-

Question Number 184305 by HeferH last updated on 05/Jan/23

i f : f (x) = x^{2} + 2 x

f i n d x :

f (f (f (x + 2))) = 99 999 999

Answered by Frix last updated on 05/Jan/23

x = t - 3

f (x) = (t - 3) (t - 1)

f (x + 2) = t^{2} - 1

f (f (x + 2)) = t^{4} - 1

f (f (f (x + 2))) = t^{8} - 1

t^{8} = 10^{8}

t = \pm 10 \lor t = \pm 10 i \lor \underset{[4 solutions]}{t = \pm 5 \sqrt{2} (1 \pm i)}

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