The sum of functions is given as:
[tex](f+g)(x)=f(x)+g(x)[/tex]
In this case we have:
[tex](f+g)(x)=5x+\sqrt[]{x-1}[/tex]
The domain of the functions is any number that makes the squared root a real number, then:
[tex]\begin{gathered} x-1\ge0 \\ x\ge1 \end{gathered}[/tex]
Hence the domain of the functions is:
[tex]\lbrack1,\infty)[/tex]
