SOLUTION: How do you find the domain of the function f(x)= 3x+1/square root of x^2+x-2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you find the domain of the function f(x)= 3x+1/square root of x^2+x-2       Log On


   

Question 1157282: How do you find the domain of the function f(x)= 3x+1/square root of x^2+x-2

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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In the denominator, you see sqrt%28x%5E2%2Bx+-+2%29.


In order for you will be able to take the square of a number, this number MUST be non-negative.


So, you first need to solve this inequality

    x%5E2%2Bx-2 >= 0.


Factor left side

    %28x-1%29%2A%28x%2B2%29 >=0.


Either both factor should be negative, or both factors should be positive.


It gives you the solution set  x <= -2  or  x >= 1.


Also, x = -2 makes the denominator equal to zero, as well as the value x = 1.


Therefore, you must exclude them from the domain.


Finally, the domain is the union of two open intervals  (-oo,-2) U (1,oo).    ANSWER

Solved.

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The "solution" by @josgarithmetic is WRONG.

Simply ignore it for your safety.