Question B 06
where a is a constant. What value of a ensures that f is continuous for all x?
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint.
What is the definition of continuity? At what x-value need we be concerned about the continuity of f?
A function is continuous at if . That is, the left-sided limit, the right-sided limit and the function value are all the same.
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
Polynomials are continuous, so the only point where we are concerned with the continuity of is . It remains to find a value such that .
Hence we need to find a value such that . It follows that the value that makes continuous on is .