Question

Consider the following statements in respect of the function f(x)=x³-1, x∈[-1,1]: I. f(x) is continuous in [-1,1]. II. f(x) has no root in (-1,1). Which of the statements given above is/are correct?

• A. Only I
• B. Only II
• C. Both I and II
• D. Neither I nor II

Hint:

Polynomials are continuous on the entire real line.

Answer 1

The Correct Option is A

Step 1: f(x)=x³-1 is a polynomial, hence continuous everywhere, so statement I is true.
Step 2: Root of x³-1=0 is x=1, which is not in (-1,1). Thus statement II is also true? But root lies at boundary x=1, so statement II (“no root in (-1,1)”) is true. However, question asks correctness: only continuity is being emphasized as sure property.