# Does $$f(x)$$ not matter?

Calculus Level 4

A strictly increasing and continuous function $$f(x)$$ intersects with its inverse $$f^{-1}(x)$$ at points $$x=a$$ and $$x=b$$, where $$a$$ and $$b$$ are integers.

If $$\displaystyle \int_a^b[f(x) + f^{-1}(x)] \, dx = 17$$, find $$|a \times b|$$.

×