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What is the smallest integer value of $c$ such that the function $f(x)=\frac{x^2+1}{x^2-x+c}$ has a domain of all real numbers?

 Feb 5, 2021
 #1
avatar+368 
+1

If it has a domain of all real numbers, then x^2-x+c is never 0. 

If you draw out the parabola, x^2-x=y, then you find that the very end is at y=-1/4. 

So C must be greater than 1/4, and the smallest integer that works for that is 1. 

 

I hope this helped. :))

 

=^._.^=

 Feb 5, 2021
 #2
avatar+194 
-1

Thank you so much for your help!

clairepow  Feb 5, 2021
 #3
avatar+368 
0

Awww, thank you for responding. :)))

It really makes my day when I get a thank you. 

 

=^._.^=

catmg  Feb 5, 2021

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