Answer:
[tex]\mathrm{Domain\:of\:}\:4\sqrt{t}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:t\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}[/tex]
The graph is also attached below.
Step-by-step explanation:
Given the expression
[tex]f\left(t\right)=\sqrt{t}\:+3\sqrt{t}[/tex]
We know that the domain of a function is the set of inputs or argument values for which the function is real and defined.
We know that we can not have a negative value of 't' inside the radicals because if we put any negative number inside the radical expression, it would make the function undefined.
In other words, the value of t ≥ 0.
Therefore, the function domain is:
[tex]\mathrm{Domain\:of\:}\:4\sqrt{t}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:t\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}[/tex]
The graph is also attached below.
