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Byju's Answer
Standard XII
Mathematics
Derivative of One Function w.r.t Another
80.If g( x) i...
Question
80.If g( x) is inverse of f( x) and domain of f is [a,b ] such that f(x)=c,f(x)=d.then prove the above integral by geometrically that graphically
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Q.
If
f
(
x
)
is a polynomial function such that
f
(
x
)
f
(
1
x
)
=
f
(
x
)
+
f
(
1
x
)
and
f
(
3
)
=
−
80
then
f
(
x
)
is equal to:
Q.
If f is an integrable function such that f(2a − x) = f(x), then prove that
∫
0
2
a
f
x
d
x
=
2
∫
0
a
f
x
d
x
Q.
Given
f
(
x
)
is a function such that
f
(
x
)
=
[
x
α
sin
1
x
i
f
x
>
0
0
i
f
x
=
0
where
α
is a constant. If
f
(
x
)
is a derivable
∀
x
≥
0
,
then the least integral value of
α
is
Q.
Let f and g be real valued functions such that f(x+y)+f(x-y)=2f(x).g(y)
∀
x
,
y
ϵ
R
. Prove that, if f(x) is not identically zero and
|
f
(
x
)
|
≤
1
∀
x
ϵ
R
, then
|
g
(
y
)
|
≤
1
∀
y
ϵ
R
.
Q.
Above shown is the graph of the function
f
(
x
)
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g
(
x
)
such that
g
(
x
)
=
1
x
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(
g
∘
f
)
(
x
)
.
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