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Byju's Answer
Standard XII
Mathematics
Definition of Functions
If f:R→ R d...
Question
If
f
:
R
→
R
defined by
f
(
x
)
=
2
x
2
−
3
x
+
5
, then find the value of
f
(
x
+
h
)
−
f
(
x
)
h
at
h
≠
0
A
4x+2h
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B
4x+2h-3
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C
4x-2h+3
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D
4x-2h-3
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Solution
The correct option is
C
4x+2h-3
Given,
f
(
x
)
=
2
x
2
−
3
x
+
5
So,
f
(
x
+
h
)
−
f
(
x
)
h
=
2
(
x
+
h
)
2
−
3
(
x
+
h
)
+
5
−
(
2
x
2
−
3
x
+
5
)
h
=
2
x
2
+
2
h
2
+
4
x
h
−
3
x
−
3
h
+
5
−
2
x
2
+
3
x
−
5
h
=
2
h
2
+
4
x
h
−
3
h
h
=
2
h
+
4
x
−
3
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0
Similar questions
Q.
Let
lim
h
→
0
h
2
f
(
x
+
2
h
)
−
2
f
(
x
+
h
)
+
f
(
x
)
=
x
1
−
x
1
+
x
(
1
+
ln
x
)
2
.
If
lim
x
→
0
+
f
(
x
)
=
1
and
f
(
1
)
=
2
,
then the value of
f
(
3
)
f
(
2
)
is
Q.
If f, g and h are three valued function defined by
f
(
x
)
=
√
x
−
1
,
g
(
x
)
=
1
x
,
h
(
x
)
=
2
x
2
+
3
find the value of
2
f
+
g
+
h
at
x
=
3
x
−
2
.
Q.
If
f
:
R
→
R
defined by
f
(
x
)
=
2
x
+
5
, if
x
>
0
;
f
(
x
)
=
3
x
−
2
, if
x
≤
0
:
then
f
is
Q.
If
f
(
x
)
=
x
2
+
2
x
+
3
,
then find
f
(
x
+
h
)
−
f
(
x
−
h
)
h
,
h
≠
0
Q.
If
1
4
(
10
h
)
−
3
2
(
h
+
1
)
=
−
2
3
(
9
2
h
)
+
6
, then the value of
h
is:
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