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Euclid R2Drew2 Edition Paper 1 · Q20

Paper 1Algebra

Let

f(x)=x2−2.f(x)=x^2-2.

Define f1(x)=f(x)f_1(x)=f(x) and, for n≥1n\geq1,

fn+1(x)=f(fn(x)).f_{n+1}(x)=f\bigl(f_n(x)\bigr).

How many distinct real solutions does the equation

f8(x)=2f_8(x)=2

have?

A6565
B127127
C128128
D129129
E256256
F255255

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