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4
1999 Calculus #4: Functional Equation
1999 Calculus #4: Functional Equation
Source:
June 21, 2012
calculus
function
Problem Statement
f
f
f
is a continuous real-valued function such that
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
f(x+y)=f(x)f(y)
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
for all real
x
x
x
,
y
y
y
. If
f
(
2
)
=
5
f(2)=5
f
(
2
)
=
5
, find
f
(
5
)
f(5)
f
(
5
)
.
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