1. find the values of s for which each function is continous:

Question

f(x) = [ x if x less than or equal to 1]
[2x-1 if x greater than 1]
2. determine all values of x at which the function is discontinuous:
f(x) = (x^2-2x)/(x^2-3x+2)

Could someone please tell me how to do these problems I'm lost.

Answer 1

1. f(x) as defined is continuous on (-∞,+∞). The only check you need to do to be sure is at x=1.
f(1-)=1
f(1+)=2*1-1=1
So f(x) is continuous also at x=1.

2.
For discontinuity of a rational function, look for values of x which render the denominator zero.
You can do this by factorization.