If f(x) is a function, what is the value of f(2)? GMAT Data Sufficiency

Question: If f(x) is a function, what is the value of f(2)?

1. 

2. 

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: D

Approach Solution (1):
S2: 

We want to find the value of f(2)
If we plug in x = ½, then 4x = (4) (1/2) = 2
So, we replace x with ½ to get: f [(4) (1/2)] = 

Simplify both sides to get: f(2) = 1
Sufficient
S1: 

This looks like it might have the features of a quadratic equation
To get a better feel, let’s let u = f(x)
So, when we take  and replace f(x) with u we get: 

Rearrange to get: 

Factor to get: 

Solve to get: u = 1
Now replace u with f(x) to get: f(x) = 1
This tells us that, for any value of x, f(x) = 1
So, we can be certain that f(2) = 1
Sufficient
Correct option: D

Approach Solution (2):

S1:

Hence sufficient
S2:
When we plug-in ½ into x, we have f(2) = \(8 (1/2)^2\) – 1 = 1
Hence sufficient
Correct option: D

Approach Solution (3):
S1
We get all the terms on LHS
It will form \((a – b)^2\)

This implies \((f(x))^2\) = 0
f(x) = 1
Hence sufficient
S2
When we plug-in ½ into x, we have f(2) = 8 \((1/2)^2\) – 1 = 1
Hence sufficient
Correct option: D

“If f(x) is a function, what is the value of f(2)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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