Posted by **Amy** on Tuesday, June 16, 2009 at 8:10pm.

Show that f is continuous on (-infinity, infinity).

f(x) = x^2 if x<1 and the square root of x if x is greater than or equal to 1.

I'm not entirely sure how to start this. Help is greatly appreciated :)

- Calculus -
**drwls**, Tuesday, June 16, 2009 at 9:21pm
f(1) = 1

For x<1, the function approaches 1 as x->1 from below.

Therefore the function is continuous at x=1. It is also defined and continuous for x>1 and x<1.

Therefore it is continuous on (-infinity, infinity)

- Calculus -
**Amy**, Tuesday, June 16, 2009 at 10:06pm
Many thanks!

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