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Range and Domain

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+194

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
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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
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Thank you so much for your help!

clairepow  Feb 5, 2021
#3
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Awww, thank you for responding. :)))

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

=^._.^=

catmg  Feb 5, 2021