Im looking at internet sites and Im not quite understanding functions. I have a question like;

Question

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.

Answer 1

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

Answer 2

thanks

Answer 3

oops wrong question