we have
[tex]f(x)=\sqrt{\frac{x}{2}-10}+3[/tex]
we know that
The domain is determined of what's under the square root sign.
so
the term [tex](\frac{x}{2}-10)[/tex] must be greater than or equal to zero
[tex]\frac{x}{2}-10 \geq 0[/tex]
Solve for x
Adds [tex]10[/tex] both sides
[tex]\frac{x}{2}-10+10 \geq 0+10[/tex]
[tex]\frac{x}{2} \geq 10[/tex]
Multiply by [tex]2[/tex] both sides
[tex]x \geq 20[/tex]
the solution is the interval---------> [20,∞)
therefore
the answer is
The inequality that can be used to find the domain of f(x) is
[tex]\frac{x}{2}-10 \geq 0[/tex]
The inequality which is used to obtained the domain, is represent below. the domain of the function f(x) is
[tex][20, \infty)[/tex].
The domain means all the possible values of the x and the range means all the possible values of y.
The function is given by,
[tex]\rm f(x) = \sqrt{\dfrac{x}{2} - 10} + 3[/tex].
We know that the value in the square root must be greater than or equal to zero. Then,
[tex]\begin{aligned} \dfrac{x}{2} - 10 &\geq 0\\\\\dfrac{x}{2} &\geq 10\\\\x &\geq 20 \end{aligned}[/tex]
Thus, the domain of the function f(x) is
[tex][20, \infty)[/tex].
More about the domain link is given below.
https://brainly.com/question/12208715
