# Find all values of c such that f is continuous

Edmund Conti 2021-12-07 Answered
Find all values of c such that f is continuous on
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## Expert Answer

Robert Harris
Answered 2021-12-08 Author has 23 answers
Since $1-{x}^{2}$ and x are continuous on $\left(-\mathrm{\infty },\mathrm{\infty }\right)$, the only possible point of discontinuity is at x=c. At this point both functions should have the same value, so
$1-{x}^{2}=x$
${x}^{2}+x-1=0$
Therefore, using quadratic formula, $x=±\frac{\sqrt{5}-1}{2}$
So the given function is continuous for $c=±\frac{\sqrt{5}-1}{2}$
Result:
$c=±\frac{\sqrt{5}-1}{2}$
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