Question
Prove that a strictly decreasing function is always one-one.
Answer :
Word Count : 147
Let ( f ) be a strictly decreasing function. By definition, for any two points ( x_1 ) and ( x_2 ) in the _______ __________ _________ ____ _____ ______.
_______ ______ ________ ___ ______ _____ _______ __________ _______ ______ _______.
___ ____ _____ _____ _____ _________ _________ __________ _____ _______.
_________ ______ _________ ______ ______ _______.
___ _____ _____ ___ _______ _____ _______ __________ __________ _______ ___ _________.
__________ ____ ___ ____ ________ _________ _____ ____ _____ ___ _________ __________.
___ ________ ________ _______ _____ ________ _______ ______ ________ ________.
_______ ___ __________ _______ ________ _____ _________ ________ _________ ______ _____.
__________ ______ ___ _____ _____ _________.
_________ _____ __________ _____ ___ _________ _______ _____.
______ _____ ________ _________ _____ __________ _________ ___ ________ _____.
_________ ______ _________ ___ _________ _________ _______ ____ ______.
_______ _____ _____ _________ _______ ________ _______.
___ _______ __________ _________ ___.
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Let ( f ) be a strictly decreasing function. By definition, for any two points ( x_1 ) and ( x_2 ) in the _______ __________ _________ ____ _____ ______.
_______ ______ ________ ___ ______ _____ _______ __________ _______ ______ _______.
___ ____ _____ _____ _____ _________ _________ __________ _____ _______.
_________ ______ _________ ______ ______ _______.
___ _____ _____ ___ _______ _____ _______ __________ __________ _______ ___ _________.
__________ ____ ___ ____ ________ _________ _____ ____ _____ ___ _________ __________.
___ ________ ________ _______ _____ ________ _______ ______ ________ ________.
_______ ___ __________ _______ ________ _____ _________ ________ _________ ______ _____.
__________ ______ ___ _____ _____ _________.
_________ _____ __________ _____ ___ _________ _______ _____.
______ _____ ________ _________ _____ __________ _________ ___ ________ _____.
_________ ______ _________ ___ _________ _________ _______ ____ ______.
_______ _____ _____ _________ _______ ________ _______.
___ _______ __________ _________ ___.
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Related Questions
Prove that a strictly decreasing function is always one-one.
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a) Determine the points of discontinuity of the function f and the nature of discontinuity at each of those points:
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Also check whether the function f is derivable at x = 1.
Using the principle of mathematical induction, show that
a) Test the following series for convergence,
(i)
(ii)
b) Show that is conditionally convergent.
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