SOLUTION: Find the domain of f, the roots of f(x)=0, and determine the signs of f where f(x)= x^2-1/sqrt x+1 + sqrt x+1

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Question 115062: Find the domain of f, the roots of f(x)=0, and determine the signs of f where

f(x)= x^2-1/sqrt x+1 + sqrt x+1

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


This function is undefined if , or putting a positive spin on the statement, the function is defined if and only if => . Therefore, the domain of the function is the interval (-1,]

The zeros of the function can be seen readily if you factor the numerator and then rationalize the denominator.





iff or or

iff , so and 1 is a zero of the function.
iff , but -1 is not in the domain of the function, therefore is undefined (notice the open ended domain interval) and -1 is not a zero of the function.
iff => , and again, -1 is not in the domain.

Therefore the only zero of the function is 1.



As to the balance of your question, "determine the signs of f where..." Where what? Re-post with the complete question and someone will try to answer.

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