Hey I got a question here involving solving for values of 3 variables that would make a parametric function contuous over a given interval. I have come up with an answer, but I want to make sure my rationale (/answer) is correct!

The question is as follows;

Off the top, the parametric function will be continuous at where the first function over is equal to the second function over , right? Ditto for the .Find all values for such that

is a continuous curve on .

Using this I did the following;

Which gives us three cases,

Next;

Substituting (Junction point)

Which shows that Case 3 is the correct case, and the values of a, b, and c that make continuous over are;

Does this look on the up and up? Thanks.