<p>For #1, the answer is indeed 18. I have a couple of methods, pick whichever one makes the most sense to you.</p>
<p>First, think of what 3*f(x-1) actually means. The (x-1) is within the function, so it is just a shift one unit to the right, which does not affect the maximum value. Therefore, the maximum value of f(x-1) is equal to the max value of f(x), which is 6. 3(6)=18, which is the answer.</p>
<p>GreedIsGood’s method of making a function also works, but a mistake was made. (x-1)^2 does not equal x^2 - 1, it equals x^2 - 2x + 1. Forgetting to factoris a common mistake, but a mistake nonetheless. I will use the same original function as GIG, -x^2 + 6 in my example. Correctly worked with calculus, the problem becomes:
y= 3(f(x-1)) = 3(-(x-1)^2 + 6) = 3(-(x^2 - 2x + 1)+6) = -3x^2 + 6x + 15
Now find max of y:
y’= -6x + 6 = 0 => x=1.
The value of 3(f(x-1)) is 18.</p>
<p>The correct answer is 18, but nonetheless, the others are correct in saying that both of these problems are much harder than one would expect to find on the SAT/PSAT.</p>