Question

Determine the value for the following recursive method when x = 19.

Answer 1

`f(19) = 2`

Step-by-step explanation:

Given

`f(x) = f(x - 5)+ 2` ---
`x > 9`

`f(x) = -2` ---
`x \le 9`

Required

Find f(19)

f(19) implies that: x = 19

Since 19 > 9, we make use of:

`f(x) = f(x - 5)+ 2`

`f(19) = f(19 - 5) + 2`

`f(19) = f(14) + 2` ----- (1)

Calculate f(14)

f(14) implies that: x = 14

Since 14 > 9, we make use of:

`f(x) = f(x - 5)+ 2`

`f(14) = f(14 - 5) + 2`

`f(14) = f(9) + 2` ------ (2)

Calculate f(9)

f(9) implies that: x = 14

Since
`9 \le 9`, we make use of:

`f(x) = -2`

`f(9) = -2`

So:

`f(14) = f(9) + 2`

`f(14) = -2 + 2`

`f(14) = 0`

`f(19) = f(14) + 2`

`f(19) = 0 + 2`

`f(19) = 2`