Description
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)
Explanation & Answer
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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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