Maybe this is a typo in our assignment and solution, but I can't tell.
The question:
The solution:
What happened here with the minus signs in the first factor and in the exponent?
Edit: the assignment asked for the fourier transform of $f(x)$. So I guess the expression highlighted in yellow is supposed to be equivalent to $f(x)$
I don't understand, what the question is.
Note however, that $|a-b| = |b-a|$ for all $a,b\in \mathbb{R}$.
The minus changing to a plus seems to be a typo though (provided the yellow colored expression is supposed to be the same as $f(x)$ for all $x\in \mathbb{R}$)