If orthogonality is defined as <f,g>=∫f(x)g(x)dx=0 where f and g are functions and the interval is on [-1,1], then we can apply this to f1 and f3 and f2 and f3. If f3 is orthogonal to both f1 and f2 then we have orthogonality.
f=f1 and f3=ax²-1: ∫(ax²-1)dx=[ax³/3-x] on [-1,1] = 2a/3-2 = 0 from which a=3.
f=f2: ∫(ax³-x)dx = [ax⁴/4-x²/2] on [-1,1] = 0 for all a because it’s an even function.
So a=3.