Question

The number of points at which the function f(x) =$\left( \frac{x^{4} + x^{2} + 1}{x^{2} + x + 1} \right)$ is discontinuous is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

3

Answer 2

The function $\log | x |$ is not defined at x = 0, so, x = 0 is a point of discontinuity. Also, for f(x) to be defined, $\log | x |$ ≠ 0 that is x ≠ ±1.

Hence, 1 and –1 are also points of discontinuity.

Clearly f(x) is continuous for x ∈ R – {0, 1, –1}.

Thus, there are three points of discontinuity