So yeah, I had a math exam today and the last question was this: f(x) = x*2^(2x+3), there is a horizontal line y=q that intersects the y axis in A and f(x) in B and C with AB:BC = 1:2. Calculate q in 2 decimals.
graph:
I didn't finish it during the exam (too bad) but this is what I came at afterwards:
f(-x) = f(-3x) ; final answer is in -x, for why take a look at the graph
-x*2^(-2x+3)=-3x*2^(-6x+3)
-x*2^(-2x)*8=-3x*2^((-2x)^3)*8
-x*2^(-2x)=-3x*2^((-2x)^3)
;;substitute p for 2^(-2x)
-xp=-3xp^3
3p^2=1
p^2=1/3
p=sqrt(1/3)
2^(-2x) = sqrt(1/3)
log2(sqrt(1/3))=-2x
-x = log2(sqrt(sqrt(1/3)))
now input log2(sqrt(sqrt(1/3))) in f and you get y=~-1.83 so q = -1.83
Did I solve this right? Are there faster or better ways to do it?
