I did not understand the question. From where this k comes?
This is something that a lot of students get confused about - the structure of function questions can be very tricky.
If the GMAT says:
If f(x) = 2x + 2, and f(m) = 8, what is the value of m?
Here's how to break down what this means:
f(x) means "the function that we perform on any given number x."
f(m) or f(k) or any other variable means "this function applied to the specific unknown number m (or k or whatever)."
So when they give you f(x), it's the general rule applied to
any x. When they follow it up with f(
any other variable), that variable is referring to a SPECIFIC number.
So here, f(f(k)) means "the function of the function of the specific number k." First, we'd figure out how to set up f(f(x)). We plug the whole function f(x) in as x:
Then, we're told that that function of k is equal to 2/3. Plug in k and simplify:
When we cross-multiply from there, we're left with:
3k = 2(2k + 1)
3k = 4k + 2
-k = 2
k = -2
The answer is
A.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
