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1984 AIME Problems
7
Another Function
Another Function
Source:
December 19, 2005
function
AMC
AIME
algebra
domain
functional equation
Problem Statement
The function
f
f
f
is defined on the set of integers and satisfies
f
(
n
)
=
{
n
−
3
if
n
≥
1000
f
(
f
(
n
+
5
)
)
if
n
<
1000
f(n)=\begin{cases} n-3 & \text{if } n\ge 1000 \\ f(f(n+5)) & \text{if } n<1000\end{cases}
f
(
n
)
=
{
n
−
3
f
(
f
(
n
+
5
))
if
n
≥
1000
if
n
<
1000
Find
f
(
84
)
f(84)
f
(
84
)
.
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