Question 127841
A word about function notation.  f or g or h is a function.  f(x) is the value of the function f at x, g(a) is the value of the function g at a.  

If {{{f(x)=1-x^2}}}, then {{{1-x^2}}} is the value of the function f at x, so f(-5) is the value of the function at -5, i.e. {{{f(-5)=1-(-5)^2}}}.  You do the arithmetic.


The domain of a function is the set of values for which the function is defined.  The given function g is a rational expression that is defined everywhere except where the denominator is zero.  So, if {{{1-2x=0}}}, then g is not defined.


{{{1-2x=0}}}


{{{-2x=-1}}}


{{{x=1/2}}}


So the domain of g is all real numbers except {{{1/2}}}.  In interval notation:


({{{-infinity}}},{{{1/2}}}) U ({{{1/2}}},{{{infinity}}})


In set notation {x|x is real, {{{x<>1/2}}}}