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Question

Let f : R R be a function. Define g:R by g(x) = |f(x)| for all x. Then g is

A
Onto if f is onto
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B
One-one if f is one-one
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C
Continuous if f is continuous
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D
None of these
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Solution

The correct option is C Continuous if f is continuous

g(x)=|f(x)|0.So g(x) cannot be onto. if f(x) one-one and f(x1)=f(x2) then
g(x1)=g(x2).
So, 'f(x) is one-one' does not ensure that g(x) is one-one.

If f(x) is continuous for xR, (x) is also continuous for xR.
This is obvious from the following graphical consideration.
So g is continuous if f is continuous.


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