Question

Solve the piece wise function when f(17)

f(x) = f(x-3)+2 if x > 10
-5 if x <= 10

Would the answer be 1? Thanks

Answer 1

I believed the answer is 16 but computer teacher is telling me it 1. Thanks

Answer 2

when x = 17
f(17) = f(14) + 2

but
f(14) = f(11) + 2

but
f(11) =f (8) + 2
but f(8) = -5 , since x ≤ 10
so f(11) = -5+2 = -3
f(14) = -3+2 = -1
f(17) = -1+2 = +1

(strange question)

Answer 3

Let say the other function is
x-2 , if x < 0
x^2 + 1 , if x >= 0

f(-4) would be -6? I kind of not understand why do we keep going down the value. Thanks

Answer 4

In this last example your function is well defined as
f(x) = x-2 or x<0 and f(x) = x^2 + 1 for x≥0
so f(-4) simply falls in the first part
f(x) = x-2
f(-4) = -4 - 2 = -6 , so you are right.

Your first problem did not have f(x) defined explicitly.
It was defined in terms of f(x-3)
so we had to find values step-by-step

Answer 5

Oh, thanks you so much! I did not realize f(x-3) and (x-3) make such different.