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
[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