Question

For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.

f(x) = sec(x) − 3.

Answer 1

A function is said to be continuous in an interval if it is defined for every value within that interval.

 

Consider the following function:

f(x) = sec(x) - 3

 

For the function f(x) = sec(x) – 3, x ≠ π/2 + kπ where k is an integer.

 

So the function is not defined at x = π/2 + kπ

 

Hence the function f(x) = sec(x) - 3 is discontinuous at x = π/2 + kπ.

 

And, the function f(x) = sec(x) – 3 is continuous for the interval (-∞, ∞) – (π/2 + kx).

So the function is not defined at x = π/2 + kπ