Question

If f(1) = 3 and f(n) = -2f(n-1)+1 what is f(4)

Answer 1

If f(1)=1 then f(f(1))=1 but f(f(1))=3, so f(1) isn't equal to 1If f(1)>2 then f(2)>3, so f(f(1))>3, but f(f(1))=3, so f(1) isn't greater than 2Thus f(1)=2, and f(2)=3f(3)=f(f(2))=6, and f(6)=f(f(3))=9, so 9 > f(5) > f(4) > 6, so f(5)=8 and f(4)=7.