SOLUTION: Find the domain of the function. State the domain in interval notation for f(x)=square root of 3x^2-x-2 I know you have to look for restrictions but I'm not sure what to do with

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Question 899350: Find the domain of the function. State the domain in interval notation for
f(x)=square root of 3x^2-x-2
I know you have to look for restrictions but I'm not sure what to do with this type of problem.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=sqrt%283x%5E2-x-2%29

The restriction starts with 3x%5E2-x-2%3E=0;
which leads to %283x%2B2%29%28x-1%29%3E=0
whose critical points are at -2/3 and 1.

You can test the signs around the critical values for x and find that the acceptable values for x are x%3C=-2%2F3 and 1%3C=x. No values of x between the critical points are acceptable in the function because they force square root of a negative number (which makes for complex solutions containing imaginary numbers).

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find the domain of the function. State the domain in interval notation for
f(x)=square root of 3x^2-x-2
I know you have to look for restrictions but I'm not sure what to do with this type of problem.


Critical points: -+2%2F3, and 1

Check the 3 intervals around the critical points, which are: x+%3C=+-+2%2F3, -+2%2F3+%3C+x+%3C+1, and x+%3E=+1. 

You should find the solution intervals to be: highlight_green%28x+%3C=+-+2%2F3%29, and highlight_green%28x+%3E=+1%29

You can do the check!! 



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