Given: f(x) = 1/2 f(x-1) - 3 and f(1) = -5 , find f(-2)

Question

I'm a tutor and I have never seen a problem like this one in honors algebra 2.  Can anyone help?

Answer 1

f(x) = (1/2)f(x-1) - 3

f(1) = (1/2)f(0) - 3 = -5 => f(0) = -4

f(0) = (1/2)f(-1) - 3 = -4 => f(-1) = -2

f(-1) = (1/2)f(-2) - 3 = -2 => f(-2) = 2 <==Answer

---------

Short cut: f(x-1) = 2(f(x)+3)

-5, 2(-5+3) = -4, 2(-4+3) = -2, 2(-2+3) = 2