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• ### $450 Tuition Credit & Official CAT Packs FREE January 15, 2019 January 15, 2019 10:00 PM PST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### The winning strategy for a high GRE score January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. # Which of the following functions satisfies f(a+b)=f(a)f(b) for all pos  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6799 GMAT 1: 760 Q51 V42 GPA: 3.82 Which of the following functions satisfies f(a+b)=f(a)f(b) for all pos [#permalink] ### Show Tags 18 Sep 2018, 01:06 00:00 Difficulty: 25% (medium) Question Stats: 74% (01:33) correct 26% (01:16) wrong based on 43 sessions ### HideShow timer Statistics [Math Revolution GMAT math practice question] Which of the following functions satisfies $$f(a+b)=f(a)f(b)$$ for all positive numbers $$a, b$$ ? $$A. f(x)=x+1$$ $$B. f(x)=x^2+1$$ $$C. f(x)=\sqrt{x}$$ $$D. f(x)=\frac{1}{x}$$ $$E. f(x)=2^x$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: Which of the following functions satisfies f(a+b)=f(a)f(b) for all pos  [#permalink]

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18 Sep 2018, 06:08
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Which of the following functions satisfies $$f(a+b)=f(a)f(b)$$ for all positive numbers $$a, b$$ ?

$$A. f(x)=x+1$$
$$B. f(x)=x^2+1$$
$$C. f(x)=\sqrt{x}$$
$$D. f(x)=\frac{1}{x}$$
$$E. f(x)=2^x$$

Upon scanning the answer choices, we might recognize that answer choice E, f(x) = 2^x, involves a variable exponent and that the given information that f(a+b) = f (a)f(b) looks A LOT like the Product Law: (k^a)(k^b) = k^(a+b)
So, let's check E first.

E. f(x) = 2^x
If f(x) = 2^x, then f(a) = 2^a, f(b) = 2^b and f(a+b) = 2^(a+b)

We get: f(a)f(b) = (2^a)(2^b)
= 2^(a+b) [apply Product Law]
= f(a+b)
PERFECT!!!

Cheers,
Brent
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Re: Which of the following functions satisfies f(a+b)=f(a)f(b) for all pos  [#permalink]

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18 Sep 2018, 07:43
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Which of the following functions satisfies $$f(a+b)=f(a)f(b)$$ for all positive numbers $$a, b$$ ?

$$A. f(x)=x+1$$
$$B. f(x)=x^2+1$$
$$C. f(x)=\sqrt{x}$$
$$D. f(x)=\frac{1}{x}$$
$$E. f(x)=2^x$$

Only E satisfies -

$$2^{a+b} = 2^a*2^b$$
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Re: Which of the following functions satisfies f(a+b)=f(a)f(b) for all pos  [#permalink]

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18 Sep 2018, 11:44
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Which of the following functions satisfies $$f(a+b)=f(a)f(b)$$ for all positive numbers $$a, b$$ ?

$$A. f(x)=x+1$$
$$B. f(x)=x^2+1$$
$$C. f(x)=\sqrt{x}$$
$$D. f(x)=\frac{1}{x}$$
$$E. f(x)=2^x$$

Another approach is to test each function to see whether f(a+b) = f(a)f(b)
For example, let's see what happens if a = 1 and b = 1
So, with each function, is it true that f(1 + 1) = f(1)f(1)?
In other words, is it true that f(2) = f(1)f(1)?

A. f(x) = x + 1
Is it true that f(2) = f(1)f(1)?
Plug values into the function to get: 2 + 1 = (1 + 1)(1 + 1)
Simplify: 3 = 4
No good.
ELIMINATE A

B. f(x) = x² + 1
Is it true that f(2) = f(1)f(1)?
Plug values into the function to get: 2² + 1 = (1² + 1)(1² + 1)
Simplify: 4 + 1 = (2)(2)
Simplify: 5 = 4
No good.
ELIMINATE B

C. f(x) = √x
Is it true that f(2) = f(1)f(1)?
Plug values into the function to get: √2 = (√1)(√1)
Simplify: √2 = (1)(1)
No good.
ELIMINATE C

D. f(x) = 1/x
Is it true that f(2) = f(1)f(1)?
Plug values into the function to get: 1/2 = (1/1)(1/1)
Simplify: 1/2 = (1)(1)
No good.
ELIMINATE D

By the process of elimination, the correct answer is E

Cheers,
Brent
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Re: Which of the following functions satisfies f(a+b)=f(a)f(b) for all pos  [#permalink]

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20 Sep 2018, 01:01
=>

$$A. f(1) = 2, f(2) = 3, f(1)f(2) = 6$$, but $$f(1+2) = f(3) = 4$$. Choice A is incorrect.
$$B. f(2) = 5, f(3) = 10, f(2)f(3) = 50$$, but $$f(2+3) = f(5) = 26$$. Choice B is incorrect.
$$C. f(9) = 3, f(16) = 4, f(9)f(16) = 12$$, but $$f(9+16) = f(25) = 5$$. Choice C is incorrect.
$$D. f(1) = 1, f(2) = \frac{1}{2}, f(1)f(2) = \frac{1}{2}$$, but$$f(1+2) = f(3) = \frac{1}{3}$$. Choice D is incorrect.
E. Let $$a,b > 0$$. Then $$f(a+b) = 2^{a+b} = 2^a2^b = f(a)f(b)$$. Choice E is correct.

Therefore, the answer is E.
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Re: Which of the following functions satisfies f(a+b)=f(a)f(b) for all pos &nbs [#permalink] 20 Sep 2018, 01:01
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# Which of the following functions satisfies f(a+b)=f(a)f(b) for all pos

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