Question

Find the x values if any at which f is not continuous f(x)={-2x+3,x<1
x^2, x>=1}

Answer 1

Both -2x+3 and x^2 are continuous because they are polynomials (and all polys are continuous)
The only thing you need to check is the at x=1 part

Answer 2

you will need the following:
f(1) exists
lim x->1 f(x) exists

And finally both of those must equal
that is you must have
f(1)=lim x->1 f(x)

Answer 3

So you might need to find the left limit and right limit as x goes to 1

Answer 4

That is check this equality:
\[\lim_{x \rightarrow 1^-}f(x) = \lim_{x \rightarrow 1^+}f(x) \]

Answer 5

If the equality holds and it is a number L that exists then \[\lim_{x \rightarrow 1}f(x)=L \]
Then you find f(1) and see if it also equals L
If so you have continuity at x=1

Answer 6

Thank you