I was given this question, and I'm not really sure how to answer it
Consider the function $f(x)=-x^2\arcsin(ax-1)+2\pi$ where a is an element of the positive real numbers
Determine the value of a such that when $f(x)=7$, the difference between the corresponding x-values is 3 (correct to 3 d.p)
I've tried to use the transformations when $a=1$ but I still haven't found the answer, when I graph it in Desmos I can find the answer, but I was asking to see if I could find the answer algebraically
Thanks!