Determine the Domain of the Function: √(5x²+2) over 10

Look at the following function:

$\frac{\sqrt{5x^2+2}}{10}$

What is the domain of the function?

To find the domain of the function $\frac{\sqrt{5x^2+2}}{10}$, we need to ensure that the expression under the square root is non-negative.

Let's examine the inequality:

This is always true since the expression $5x^2$ (a non-negative value for all real $x$) added to 2 will always be greater than or equal to zero. Consequently, $5x^2 + 2$ never takes a negative value, confirming the square root is always defined.

Therefore, the function $\frac{\sqrt{5x^2+2}}{10}$ is defined for all real numbers.

In conclusion, the domain of the function is all real numbers.