Explanation
Give that
[tex]\begin{gathered} f(x)=\frac{1}{x} \\ \\ g(x)=\frac{x+1}{3} \end{gathered}[/tex]
To get the value of
[tex](fog)(x)[/tex]
we will have
[tex](f\text{ o g})(x)=f\left(\frac{x+1}{3}\right)=\frac{3}{x+1}[/tex]
The value (f o g) (x) is
[tex]\left(fog\right)x=\frac{3}{x+1}[/tex][tex]The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values\:for\:which\:the\:function\:is\:real\:and\:defined[/tex]
The graph is
Thus, the Domain is
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x<-1\quad \mathrm{or}\quad \:x>-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-1\right)\cup \left(-1,\:\infty \:\right)\end{bmatrix}[/tex]
