Linear function . What is the increasing linear function if f(f(x))=4x+3 ?

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An increasing linear function is of the form y = ax + b where a is positive.

It is given that f(f(x))=4x+3

=> f(ax + b) = 4x + 3

=> a(ax + b) + b = 4x + 3

=> a^2x + ab + b = 4x + 3

=> a^2 = 4 and ab + b= 3

=> a = 2, a = -2 is rejected as a is positive.

=> 2b + b = 3

=> 3b = 3

=> b = 1

The function is f(x) = 2x + 1

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