# surjectivity

• May 2nd 2010, 04:32 PM
alexandrabel90
surjectivity
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, 05:36 PM
rubic
[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
• May 5th 2010, 08:50 PM
dwsmith
Quote:

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?