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If f(x+y) = f(x)f(y), what is the value of f(0)? 1) f(x) > 0 2) f(x) h

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If f(x+y) = f(x)f(y), what is the value of f(0)? 1) f(x) > 0 2) f(x) h [#permalink]

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[GMAT math practice question]

If f(x+y) = f(x)f(y), what is the value of f(0)?

1) f(x) > 0
2) f(x) has integer values
[Reveal] Spoiler: OA

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Re: If f(x+y) = f(x)f(y), what is the value of f(0)? 1) f(x) > 0 2) f(x) h [#permalink]

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1) Put y = 0: f(x+0) = f(x) = f(x)*f(0), Divide both sides by f(x) which is not equal to zero (so we can divide), f(0) ends up being equal to 1, sufficient.
2) f(x) can be 0, which doesn't let me do the procedure above + no info given about f(y) or any other combination, insufficient.

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Re: If f(x+y) = f(x)f(y), what is the value of f(0)? 1) f(x) > 0 2) f(x) h [#permalink]

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New post 12 Nov 2017, 19:00
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Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

To find the value of f(x), we can plug in 0 for the variables x and y.
Then we have \(f(0+0) = f(0) ∙ f(0) or f(0) = {f(0)}^2\)
\({f(0)}^2 - f(0) = 0\)
\(f(0) { f(0) – 1 } = 0\)
Then \(f(0) = 0 or f(0) = 1.\)
Then f(0) becomes an unknown variable and we have 1 variable. D is most likely to be the answer.
Condition 1)
Since f(0) > 0, we have f(0) = 1.
This is sufficient.

Condition 2)
Both 0 and 1 are integers, f(0) = 0 or f(0) = 1.
Thus, this is not sufficient.

Therefore, A is the answer.
Answer: A
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Re: If f(x+y) = f(x)f(y), what is the value of f(0)? 1) f(x) > 0 2) f(x) h   [#permalink] 12 Nov 2017, 19:00
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