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Is the function f:R→R defined by f(x)=cos(2x+1) invertible?Give reasons.Can you modify domain and codomain of f such that f becomes invertible?
Dear Menka,
no the function is not invertible as the function f(x) is not BIJECTIVE as it is not one to one
as there are many values of x for which there exist values of -1 to 1 the range of the function
and the function is also not onto as the codomain is all real number R but the range of f(x) is -1 to 1
and for onto the codomain must be equal to range .
as we know the necessary and sufficient condition for the function to be invertible should be
that the function must be bijective .
to make function invertible the codomain must be equal to [-1 , 1]
and domain must be
0 <= 2x + 1 <= pie
now by this relation we get
-1/2 <= x <= (pie - 1 )/2
so the domain must be equal to -1/2 <= x <= (pie - 1 )/2
and codomain is [-1 , 1]. to make function invertible
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jitender
Hi Menka,
Here's the answer in the scanned copy:
Hope that helps.
All the best.
Regards,
Ashwin (IIT Madras).
hi ashwin
i did not get the first part of the solution was it asked
and i think i have done the problem in simpler way
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