Question

F(x+2)=2(2f(x)+1), f(2)=4, f(6)=?

Answer 1

$f(2)=4\\\\f(x+2)=2\cdot (2\cdot f(x)+1)\\\\a)\; \; x=2\; ,\; f(2+2)=2\cdot (2\cdot f(2)+1)\\\\f(4)=2\cdot (2\cdot 4+1)\\\\f(4)=18\; ,\\\\b)\; \; x=4\; ,\; f(4+2)=2\cdot (2\cdot f(4)+1)\\\\f(6)=2\cdot (2\cdot 18+1)\\\\f(6)=74$

Answer 2

To find the value of f(6), we can use the information given and work step by step. Let's solve the problem:

1. Given: F(x + 2) = 2(2f(x) + 1)

2. Given: f(2) = 4

First, let's find f(4) using f(2):

F(2 + 2) = 2(2f(2) + 1) F(4) = 2(2 * 4 + 1) F(4) = 2(8 + 1) F(4) = 2 * 9 F(4) = 18

Now, let's find f(6) using f(4):

F(4 + 2) = 2(2f(4) + 1) F(6) = 2(2 * f(4) + 1) F(6) = 2(2 * 18 + 1) F(6) = 2(36 + 1) F(6) = 2 * 37 F(6) = 74

So, the value of f(6) is 74.