Consider the following function $$f(x) = \left\{\begin{array}-(a^2 - x^2)^{1/2} & \text{if }|x|\leq a \\+ \infty &\text{otherwise}\end{array}\right.$$ and compute its Legendre transform.
I solved the above questions, however, I can't solve the question that the infinite in the function. How can I apply the Legendre transform to this question?