surjectivity

**alexandrabel90** · May 2nd 2010, 03:32 PM

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

**rubic** · May 2nd 2010, 04:36 PM

[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 $y^{-1} : R->$ (0 to infinity)
$y = |log (x)|$
$e^{y} = e^{ log x}$
$x = e^{y}$
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

**dwsmith** · May 5th 2010, 07:50 PM

Originally Posted by alexandrabel90

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

The range is $(-\infty,\infty)$ . Now what does f(x) = -10 map to in the domain?

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