Question

If f (x) = StartRoot one-half x minus 10 EndRoot + 3, which inequality can be used to find the domain of f(x)?

Answer 1

Answer:

(1/2) x - 10 + 3 > 0is the inequality that can be used to find the domain of given f(x).

Step-by-step explanation:

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Answer 2

Given :   $f(x)=\sqrt{\dfrac{1}{2} x-10} +3$

To Find : Domain of x

$\sqrt{\dfrac{1}{2} x} ~ \geq 0$

$\dfrac{1}{2} x ~ \geq 0$

 $\dfrac{1}{2} x -10 ~ \geq 0$

$\sqrt{\dfrac{1}{2} x-10} + 3~ \geq 0$

Solution:

Domain of the function are the values for which function is defined

$f(x)=\sqrt{\dfrac{1}{2} x-10} +3$

Square root of negative numbers are not defined Hence value inside square root must be greater than equal to zero

$\sqrt{\dfrac{1}{2} x-10}$  

Hence

$\dfrac{1}{2} x -10 ~ \geq 0$

Correct answer is  $\dfrac{1}{2} x -10 ~ \geq 0$

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