Answer:
Domain [tex]=(-\infty,\ \infty)[/tex]
Range [tex]=(-\infty,\ \infty)[/tex]
Step-by-step explanation:
Domain : Domain of a function [tex]f(x)[/tex] is the set of all possible values of [tex]x[/tex] for which [tex]f(x)[/tex] exists.
Range : range of a function [tex]f(x)[/tex] is the set of all possible values of [tex]f(x)[/tex].
Here [tex]f(x)=36-3x[/tex]
[tex]x[/tex] can be any value from [tex]-\infty[/tex] to [tex]\infty[/tex].
[tex]\forall\ x=a\ there\ exists\ f(x)\ such\ that\ f(a)=36-3a[/tex]
hence possible value of [tex]x[/tex] can be any value between [tex]-\infty[/tex] and [tex]\infty[/tex]
[tex]domain =(-\infty,\ \infty)[/tex]
let [tex]y=-f(x)[/tex]
[tex]y=36-3x\\3x=36-y\\\\\\x=\frac{36-y}{3}\\[/tex]
so [tex]\forall\ f(x)=y\ there\ exist\ x\ \in(-\infty,\ \infty)[/tex].
hence [tex]f(x)[/tex] can have any value between [tex]-\infty\ to\ \infty.[/tex].
Range [tex]=(-\infty,\ \infty)[/tex]
