Functions in Math
posted by Lena on .
Im looking at internet sites and Im not quite understanding functions. I have a question like;
A function f(x) has the properties
i) f(1) = 1
ii) f(2x) = 4f(x)+6
Could you help me out. I know nothing about functions.

Differentiate both sides of:
f(2x) = 4f(x)+6 >
f'(2x) = 2f'(x) >
f'(x) = a x >
f(x) = b x^2 + c
Insert this in the functional equation to find that c = 2
The first equaton f(1) = 1 then gives:
f(x) = 3 x^2  2 
thanks

oops wrong question