The function f(x) has property that f(2x + 3) = 2 f(x) + 3, x∈R.

If f(0) = 6, find the value of:

a. f(3)

b. f(9)

c. f(-3)

Thank you for the opportunity to help you with your question!

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f(2x + 3) = 2f(x) + 3

f(0) = 6

We can find f(3) by putting x = 0

f(2*0 + 3) = 2f(0) + 3

f(3) = 2*6 + 3

f(3) = 12 + 3

f(3) = 15

We can find f(9) by putting x = 3

f(2*3 + 3) = 2f(3) + 3

f(6 + 3) = 2*15 + 3

f(9) = 30 + 3

f(9) = 33

We can find f(-3) by putting x = -3

f(2*(-3) + 3) = 2f(-3) + 3

f(-6 + 3) = 2f(-3) + 3

f(-3) = 2f(-3) + 3

f(-3) - 2f(-3) = 3

-f(-3) = 3

f(-3) = -3

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