f(x) = (x^2 + cos x)/(x^2 + 1)

Question

Find the points of discontinuity, if any, for the following:

\(f(x) = \frac{x^2 + cos\,x}{x^2 + 1}\)

f(x) = (x² + cos x)/(x² + 1)

Answer 1

f(x) = (x² + cos x)/(x² + 1)

Here, x² is always continuous for all real values of x and cosine is a continuous function

\(\therefore\) p(x) is a continuous function and q(x) = x² + 1

It is a polynonimal function

\(\therefore\) It is continuous for all real values of x

\(\therefore\) f(x) is a continuous function.