Answer:
The range of the function [tex](g\°f)(x)[/tex] is
B. is all real numbers except [tex]y=0[/tex]
Step-by-step explanation:
Given functions:
[tex]f(x)=x+3[/tex]
[tex]g(x)=\frac{1}{x}[/tex]
To find the range of [tex](g\°f)(x)[/tex].
Solution:
In order to find [tex](g\°f)(x)[/tex] , we will plugin [tex]f(x)[/tex] in function [tex]g(x)[/tex].
[tex](g\°f)(x)=g(f(x))[/tex]
[tex](g\°f)(x)=\frac{1}{x+3}[/tex]
The graph of the function [tex](g\°f)(x)[/tex] shows that
1) As [tex]x[/tex] approaches -3 (but never touches the line [tex]x=-3[/tex]), [tex]y[/tex] tends to positive or negative infinity.
2) As [tex]y[/tex] approaches 0 (but never touches the line [tex]y=0[/tex]) , [tex]x[/tex] tends to positive or negative infinity.
Thus, the range of the function is all real numbers except [tex]y=0[/tex]
