We have the following functions:
[tex]\begin{gathered} f(x)=3x \\ f(x)=\sqrt[]{x} \\ f(x)=3x+4 \\ f(x)=\frac{1}{\sqrt[]{x-3}} \end{gathered}[/tex]notice that on the first and the third case, the functions are linear, thus, their domain is the set of real numbers.
The second function is a square root function, which has the set of positive real numbers as its domain.
Finally, we can see that on the last function, the denominator becomes 0 when x = 3. And also, if x is less than 3, we get a negative number inside the square root, which cant happen in this case. Therefore, its domain is the set of real numbers greater than 3.
