Respuesta :
[tex]\left(\frac{1}{2}\right) x-10+3 \geq 0[/tex] is the inequality that can be used to find the domain of given f(x).
Step-by-step explanation:
For a square root function given by [tex]f(x)=\sqrt{a(x)}[/tex], to have real values, the radicand x must be positive or equal to zero. So, domain for f(x) would be,
[tex]a x \geq 0[/tex]
Given:
[tex]f(x)=\sqrt{\left(\frac{1}{2}\right) x-10}+3[/tex]
In the given expression, under the square root, in place of ‘x’ presents as below and so
[tex]\left(\frac{1}{2}\right) x-10+3 \geq 0[/tex]
The inequality depends on the true form of the given term, so it should be,
[tex]\left(\frac{1}{2}\right) x-10+3 \geq 0[/tex]
The domain of a function is indeed the collection of any and all possible inputs to a function. So, the calculation of the domain can be defined as follows:
Given:
[tex]\to \bold{f(x)=\sqrt{\frac{1}{2} x-10}+3}[/tex]
To find:
Domain=?
Solution:
The domain of a function is the set of values for which the behavior is described.
[tex]\to \bold{f(x)=\sqrt{\frac{1}{2} x-10}+3}[/tex]
There is no concept for the quadratic formula of negative territory. As a result, the value within the square root has to be greater than zero.
Hence
[tex]\to \bold{f(x)=\sqrt{\frac{1}{2} x-10} \geq 0}[/tex]
Therefore, the correct answer is "[tex]\bold{\sqrt{\frac{1}{2} x-10}\geq 0}[/tex]".
Learn more:
brainly.com/question/14736754
