Question 1026181
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6. (a) Find the domain of the function
f(x) = {x / sqrt (5-3x) + x sqrt (x + 1)} 
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When you see a square root, and you are asked about the domain, take care that the function under the square root is non-negative.

So, in this case these two inequalities must be held:

5-3x > 0,    (1)   and
x+1   = 0.   (2).

Notice that in (1) I wrote the strong inequality.
It is because we have {{{sqrt(5-3x)}}} in the denominator.


Now, from (1),  5 > 3x,  x < {{{5/3}}}.

From (2),  x >= -1.


So, the answer is -1 <= x < {{{5/3}}}.


It is the semi-segment  [-1, {{{5/3}}}).


The domain is the semi-segment  [-1, {{{5/3}}}).
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