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 (,).f(x)={1x2,xc {x,x>c
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Expert Answer

Robert Harris
Answered 2021-12-08 Author has 23 answers
Since 1x2 and x are continuous on (,), the only possible point of discontinuity is at x=c. At this point both functions should have the same value, so
1x2=x
x2+x1=0
Therefore, using quadratic formula, x=±512
So the given function is continuous for c=±512
Result:
c=±512
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