- For all positive integers p and q, let the function p♮q be defined as p♮q = 2p-q. If g♮12 = g, then g =
The cardinal rule of function questions is this: FOLLOW THE DIRECTIONS EXACTLY.
If p♮q = 2p-q, then g♮12 = 2g-12. We know that’s equal to g. Here’s what we have so far:
From here, we COULD start listing powers of 2 to see which ones might work, or we could take a shortcut and BACKSOLVE because we know one of the 5 answer choices has to be right. I vote the latter. As always when backsolving, start with (C). That says:
Note that 8 is too small…it creates a negative exponent on the left of our equation. So let’s move towards (D) and see what happens:
BOOM GOES THE DYNAMITE.
(D) is our answer.