A continuous function is a type of mathematical function that has no sudden or abrupt changes in its values. This means that the graph of the function has no breaks, holes, or gaps.
The general method for solving continuous functions involves finding the value of the function at a given point, and then using the limit definition of continuity to find the value of the function at that point.
To find the value of g(3), you can use the limit definition of continuity to set up an equation with two unknowns (g(3) and the limit) and then solve for g(3).
The limit represents the value that g(x) approaches as x approaches 3. Therefore, the value of g(3) must be equal to the limit in order for the function to be continuous at x=3.
Yes, in order for g(3) to have a unique solution, f(3) must be equal to the limit. If f(3) is not equal to the limit, then there will be multiple possible values for g(3).