Question

Identify discontinuities for the following functions as either a jump or a removable discontinuity.

f(x) = 4 + sin x, for x < π = 3 – cos x for x > π.

Answer 1

f(x) = 4 + sin x, for x < π = 3 – cos x for x > π.

sin x and cos x are continuous for all x ∈ R. 

4 and 3 are constant functions. 

∴ 4 + sin x and 3 – cos x are continuous for all x ∈ R. 

∴ f(x) is continuous for both the given intervals.

Let us test the continuity at x = π.

But f(π) is not defined. 

∴ f(x) has a removable discontinuity at x = π.