Question

Let f(x)=sin²x, x is rational

Let f(x)=−sin²x, x is irrational,

then set of points, where f (x) is continuous, is:
A. {(2n+1)π/2∈I}
B. a null set
C. {nπ,n∈I}
D. set of all rational numbers

Answer 1

The correct answer from the given option is D. The set of points where f(x) is continuous is the set of all rational numbers.

Step-by-step explanation:

To find the set of points where f(x) is continuous, we need to consider the values of x that make the function definition switch from sin²x to -sin²x or vice versa.

When x is rational, the function is defined as sin²x and when x is irrational, the function is defined as -sin²x. The function is continuous when there are no sudden changes in definition, so the set of points where f(x) is continuous is the set of all rational numbers.