MathDB
Problems
Contests
National and Regional Contests
India Contests
ISI Entrance Examination
2013 ISI Entrance Examination
3
3
Part of
2013 ISI Entrance Examination
Problems
(1)
|f(x+y)-f(x-y)-y|<=y^2 for all x,y
Source: ISI Entrance exam 2013, P3
5/12/2013
Let
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
satisfy
∣
f
(
x
+
y
)
−
f
(
x
−
y
)
−
y
∣
≤
y
2
|f(x+y)-f(x-y)-y|\leq y^2
∣
f
(
x
+
y
)
−
f
(
x
−
y
)
−
y
∣
≤
y
2
For all
(
x
,
y
)
∈
R
2
.
(x,y)\in\mathbb R^2.
(
x
,
y
)
∈
R
2
.
Show that
f
(
x
)
=
x
2
+
c
f(x)=\frac x2+c
f
(
x
)
=
2
x
+
c
where
c
c
c
is a constant.
inequalities
function
real analysis
real analysis unsolved