I struggled with the last question too, my maths teacher explained it and got a=50, b=50 and k=4. The answers are different from the mark scheme, but there are a lot of errors in that so we aren't 100% trusting of it.
I vaguely understand some of it, I get how k=4 as because of f(ax), it is compressed horizontally by 1/4. But I don't quite get the rest, hopefully someone else will be able to explain it on here! :)