How do you find the x values at which f(x)=3x-cosx is not continuous, which of the discontinuities are removable?

1 Answer
Dec 8, 2016

f(x)=3x-cosx is continuous AA x in RR, and so it does not have any discontinuities.

Explanation:

3x is continuous for all real numbers x (we write as AA x in RR which means for all x in the set of real numbers).

cosx is also continuous AA x in RR

Therefore any linear combination of the above is also continuous AA x in RR.

Hence f(x)=3x-cosx is continuous AA x in RR, and so it does not have any discontinuities.

You can see this visually by looking at the graph of y)=3x-cosx, which is essentially that of y=3x with a slight oscillation caused by the addition of -cosx

graph{3x-cosx [-30, 30, -30, 30]}