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What is the smallest integer value of c such that the function f(x) = (x^2 + 1)/(x^2 + 1 + c) has a domain of all real numbers?

 Jun 11, 2022
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Note that the function will not have a domain of all real numbers when the denominator has a real solution for x. 

 

This means we are looking for the smallest number where the roots of \(x^2 +1 + c = 0\) are imaginary. 

 

The smallest number in which this is satisfied is \(\color{brown}\boxed{0}\)

 Jun 11, 2022

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