F (x) = ax + B, and f (f (x)) = 4x-1, find f (x)

F (x) = ax + B, and f (f (x)) = 4x-1, find f (x)

Because f (x) = ax + B
Then: F [f (x)] = f (AX + b) = a (AX + b) + B = a * a * x + AB + B = 4x-1
So a * a = 4, a = ± 2
When a = 2, AB + B = 2B + B = - 1, B = - 1 / 3
∴f(x)=2x-1/3
When a = - 2, AB + B = - 2b + B = - 1, B = 1
∴f(x)=-2x+1
The analytic expression of F (x) is (x) = 2x-1 / 3 or (x) = - 2x + 1

Elden Ring Premiere

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