Question

The function f(x) = `(x + 1)/(9x + x^3)` is.

Options

• discontinuous at exactly two points

• discontinuous at exactly one point

• continuous for all real values of x

• discontinuous at exactly three points

Answer 1

discontinuous at exactly one point

Explanation:

We have,

f(x) = `(x + 1)/(9x + x^3)`

f(x) is not defined at 9x + x³ = 0

x(9 + x²) = 0

x = 0, 9 + x² ≠ 0 

∴ f(x) is discontinuous at x = 0

Hence, f(x) is continuous of exactly one point.