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

1 Answer
Steve M
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]}

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