Answer:
![f(19) = 2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/fsud6n138lcgj34xpqn5pa912lvvdgaihq.png)
Step-by-step explanation:
Given
---
![x > 9](https://img.qammunity.org/2022/formulas/computers-and-technology/college/bhzvd2el457bmpyyf6tihp8xmccp3w4vxt.png)
---
![x \le 9](https://img.qammunity.org/2022/formulas/computers-and-technology/college/uz822ubu63b4jrpi9w1q7a66cih0eh0rdy.png)
Required
Find f(19)
f(19) implies that: x = 19
Since 19 > 9, we make use of:
![f(x) = f(x - 5)+ 2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/2w8mn01c0b3z665m60b3mzyjs7x4i8yaq9.png)
![f(19) = f(19 - 5) + 2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/cvo6asuwt0mxo9jfuy5y6pl2avf7l21jo2.png)
----- (1)
Calculate f(14)
f(14) implies that: x = 14
Since 14 > 9, we make use of:
![f(x) = f(x - 5)+ 2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/2w8mn01c0b3z665m60b3mzyjs7x4i8yaq9.png)
![f(14) = f(14 - 5) + 2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/12pjdhfl3fk6m1aca04pj0griaxhporrv0.png)
------ (2)
Calculate f(9)
f(9) implies that: x = 14
Since
, we make use of:
![f(x) = -2](https://img.qammunity.org/2022/formulas/mathematics/college/pktg19ir24qdu7c4yyn8e4mohs6ye0l4gk.png)
![f(9) = -2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/6x7knxpiwo7x4br402018o2ql2ax4xgi2r.png)
So:
![f(14) = f(9) + 2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/krzplpvbmikmsbuo4x8siji55bsoup3xxp.png)
![f(14) = -2 + 2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/zo2idymb1hhcjcxk4i6eohrxoabxburv8z.png)
![f(14) = 0](https://img.qammunity.org/2022/formulas/computers-and-technology/college/u88itn17k3l0ei0ec9ovvwh3z2d0jw0yyx.png)
![f(19) = f(14) + 2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/4csvtly0xnnof4124il1da6fogfhzf62l3.png)
![f(19) = 0 + 2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/nwoh4r7icvesi6vfmb0otubbguzhfiw7wi.png)
![f(19) = 2](https://img.qammunity.org/2022/formulas/computers-and-technology/college/fsud6n138lcgj34xpqn5pa912lvvdgaihq.png)