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Functions in Math

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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.

  • Functions in Math -

    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

  • Functions in Math -

    thanks

  • Functions in Math -

    oops wrong question

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