Question 405429
Please put parentheses around radicands (the expressions within a radical). For example:
g(x) = square root(5x+2)
What you posted could be interpreted as
{{{g(x)  = sqrt(5x+2)}}}
or
{{{g(x)  = sqrt(5x)+2}}}
which are different functions with different domains.<br>
From your attempted solution, I guess that the correct function is:
{{{g(x)  = sqrt(5x+2)}}}
The domain of this function will be all the numbers that make the radicand non-negative (positive or zero). So you just solve the inequality:
{{{5x+2 >=0}}}
Subtract 2 from each side:
{{{5x >= -2}}}
Divide by 5:
{{{x >= -2/5}}}
This is the domain. In interval notation this is:
[{{{-2/5}}}, {{{infinity}}})