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Mathematics
Problem
Let
f
:
R
→
R
f: R \to R
f
:
R
→
R
be a function which satisfies
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
∀
x
,
y
∈
R
.
If
f
(
1
)
=
2
and
f(x+y) = f(x) + f(y) \quad \forall x, y \in R. \text{ If } f(1) = 2 \text{ and}
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
∀
x
,
y
∈
R
.
If
f
(
1
)
=
2
and
g
(
n
)
=
∑
k
=
1
n
−
1
f
(
k
)
,
n
∈
N
,
then the value of
n
,
g(n) = \sum_{k=1}^{n-1} f(k), \quad n \in N, \text{ then the value of } n,
g
(
n
)
=
k
=
1
∑
n
−
1
f
(
k
)
,
n
∈
N
,
then the value of
n
,
for which
g
(
n
)
=
20
g(n) = 20
g
(
n
)
=
20
is (a) 5 (b) 20 (c) 4 (d) 9
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