Answer:
The domain of the function [tex]g(x)[/tex] is greater than the domain of the function [tex]f(x).[/tex]
Step-by-step explanation:
The diagram shows the logarithmic function [tex]f(x)[/tex]. The domain of this function is
[tex]x>-3[/tex]
The domain of the square root function [tex]g(x)=\sqrt{x+3}+1[/tex] is
[tex]x+3\ge 0\\ \\x\ge -3[/tex]
The domain of the function [tex]g(x)[/tex] is greater than the domain of the function [tex]f(x),[/tex] because the set [tex]x\ge -3[/tex] contains the set [tex]x>-3[/tex] ( [tex](-3,\infty)\subset [-3,\infty)[/tex]).
