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Byju's Answer
Standard XII
Mathematics
Basic Inverse Trigonometric Functions
how can we pr...
Question
how can we prove that a function is invertible?
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Solution
Prove that the function is injective i.e it is one-one as well as onto
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Similar questions
Q.
Prove that the function
f
:
[
0
,
∞
)
→
R
given by
f
(
x
)
=
9
x
2
+
6
x
−
5
is not invertible. Modify the codomain of the function f to make it invertible, and hence find
f
−
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Q.
Prove that the function
f
:
R
→
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x
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=
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,
is invertible and find the inverse of
f
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Q.
Prove that the function
f
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[
0
,
∝
)
→
R
given by
f
(
x
)
=
9
x
2
+
6
x
−
5
is not invertible.
Q.
How can we prove that matter is made of particles?
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If the function
f
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=
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2
x
−
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is invertible then find its inverse. Hence prove that
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o
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−
1
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x
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