First of all, we can just ignore A, it has no effect but to vertically stretch our cosine.
If it was only [tex]f(x)=cosx[/tex], the function would be invertible as long as it's confined between [tex] 0[/tex] and [tex]\pi[/tex]. Now, the argument of our cosine is not [tex]x[/tex] but [tex]bx[/tex]. It means that it won't stop at [tex]\pi[/tex], but at [tex]\frac{\pi}{b}[/tex].
Another way to think about it, "what should i replace x with so I get [tex]\pi[/tex] inside the cosine?"
