Carcass wrote:
If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one possible value of k?
A. √2
B. 2
C. 4
D. 2√2
E. 14
STRATEGY: As with all GRE Multiple Choice questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can test each answer choice by plugging it into the function to see which value satisfies the equation f(2k) = 36.
So, that's one option.
Now we should give ourselves 15-20 seconds to identify a faster approach.
In this case, we can also solve the equation.
I'm pretty sure I can quickly solve the equation so I'm going to go with that approach. If
f(x)=x2+4, then
f(2k)=(2k)2+4=4k2+4Since we are told
f(2k)=36, we can write:
4k2+4=36Divide both sides of the equation by
4 to get:
k2+1=9Subtract
1 from both sides to get:
k2=8So, EITHER
k=√8 OR
k=−√8Check the answer choices...... Not there. It looks like we need to simplify
√8√8=√4×2=√4×√2=4√2.
So, EITHER
k=2√2 OR
k=−2√2Answer: D