Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter Relations and Functions. This page offers a step-by-step solution to the specific question from Exercise 2, Question 1: . With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.
Show that the function f : R* → R* defined by f(x) = 1/x is one-one and onto,where R* is the set of all non-zero real numbers. Is the result true, if the domain R* is replaced by N with co-domain being same as R* ?
It is given that f: R* → R* is defined by
One-one:
∴f is one-one.
Onto: It is clear that for y∈R*, there exists 
such that
∴f is onto.
Thus, the given function (f) is one-one and onto.
Now, consider function g: N → R* defined by
We have,
∴g is one-one.
Further, it is clear that g is not onto as for 1.2 ∈R* there does not exit any x in N such that g(x) =
.
Hence, function g is one-one but not onto.
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Read MoreWelcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 2 , Question 1: Show that the function f : R* → R* defined by f(x) = 1/x is one-one and onto,where R*....
be a function defined as
. The inverse of f is map g: Range
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Give solution of continuity and differentiability