given that the function f(x) = l log x l where the domain is (0, infinity) and the range is real numbers. may i know why is the function not surjective?

thanks

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- May 2nd 2010, 03:32 PMalexandrabel90surjectivity
given that the function f(x) = l log x l where the domain is (0, infinity) and the range is real numbers. may i know why is the function not surjective?

thanks - May 2nd 2010, 04:36 PMrubic
[quote=alexandrabel90;505619]given that the function f(x) = l log x l where the domain is (0, infinity) and the range is real numbers. may i know why is the function not surjective?

if y has an inverse $\displaystyle y^{-1} : R->$(0 to infinity)

$\displaystyle y = |log (x)|$

$\displaystyle e^{y} = e^{ log x}$

$\displaystyle x = e^{y}$

surjective = the range is equal to the codomain

simply because y can only take positive values, so there are some elements in range(R) which are not covered - May 5th 2010, 07:50 PMdwsmith