how to find the continuity of this function? f(x)=1-3x^2

To determine the continuity of a function, we need to check three conditions:

1. The function must be defined at the given point.
2. The limit of the function as it approaches the given point must exist.
3. The value of the function at the given point must be equal to the limit.

In this case, we have the function f(x) = 1 - 3x^2. To find the continuity of this function, we need to check its behavior at all points in its domain.

First, let's consider the points where the function is not defined. In this case, there are no such points, as the function is defined for all real numbers x.

Next, let's check the limits of the function as it approaches different points. Since the function is a polynomial, the limits as x approaches any value will exist.

Finally, let's evaluate the value of the function at the given points and compare it to the limit. For example, let's consider a point x = a. We need to check if f(a) equals the limit as x approaches a.

To do this, substitute x = a into the function f(x) = 1 - 3x^2 and evaluate it. Compare this value to the limit as x approaches a. If they are equal, then the function is continuous at x = a.

Repeat this process for all points in the domain of the function to determine the continuity of the function.