Question

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

Answer 1

Answer:

$f(19) = 2$

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:

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

$f(14) = -2 + 2$

$f(14) = 0$

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

$f(19) = 0 + 2$

$f(19) = 2$