Ok, a fun hack
if f⁻¹(a)=b then f(b)=a
so if f⁻¹(7)=b then f(b)=7
to find b, find x such that f(x)=7
7=0.5(3)^x
times both sides by 2 (or divide both sides by 0.5)
14=3^x
take log₃ of both sides

For part A Amy's estimate is inaccurate because when adding fractions they must have the same denominators. Amy probably made the mistake of adding 1/4 and 1/3 without changing the denominators first which gave her 1/7. If she were to do it correctly then she would've ended up with 7/12 as her answer.
My work:
1/4=3/12
1/3=4/12
4/12+3/12=7/12
I hope this helps and if I gave any false information I apologize in advance.
The GCF is 5
Hope this helps