Answer:
[tex]f(19) = 2[/tex]
Explanation:
Given
[tex]f(x) = f(x - 5)+ 2[/tex] --- [tex]x > 9[/tex]
[tex]f(x) = -2[/tex] --- [tex]x \le 9[/tex]
Required
Find f(19)
f(19) implies that: x = 19
Since 19 > 9, we make use of:
[tex]f(x) = f(x - 5)+ 2[/tex]
[tex]f(19) = f(19 - 5) + 2[/tex]
[tex]f(19) = f(14) + 2[/tex] ----- (1)
Calculate f(14)
f(14) implies that: x = 14
Since 14 > 9, we make use of:
[tex]f(x) = f(x - 5)+ 2[/tex]
[tex]f(14) = f(14 - 5) + 2[/tex]
[tex]f(14) = f(9) + 2[/tex] ------ (2)
Calculate f(9)
f(9) implies that: x = 14
Since [tex]9 \le 9[/tex], we make use of:
[tex]f(x) = -2[/tex]
[tex]f(9) = -2[/tex]
So:
[tex]f(14) = f(9) + 2[/tex]
[tex]f(14) = -2 + 2[/tex]
[tex]f(14) = 0[/tex]
[tex]f(19) = f(14) + 2[/tex]
[tex]f(19) = 0 + 2[/tex]
[tex]f(19) = 2[/tex]
