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Math Expert V
Joined: 02 Sep 2009
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If f(a)=a2, what is the value of f(a+b)−f(a) b ? a b 2a 2a +  [#permalink]

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Question Stats: 86% (01:10) correct 14% (01:19) wrong based on 79 sessions

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If f(a)=a^2, what is the value of (f(a+b)−f(a))/b ?

A. a
B. b
C. 2a
D. 2a + b
E. 2b - a

Kudos for correct solution.

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If f(a)=a2, what is the value of f(a+b)−f(a) b ? a b 2a 2a +  [#permalink]

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Bunuel wrote:
If f(a)=a^2, what is the value of (f(a+b)−f(a))/b ?

A. a
B. b
C. 2a
D. 2a + b
E. 2b - a

Kudos for correct solution.

start with f(a+b) before start calculations: f(a+b)=(a+b)^2= a^2+2ab+b^2

a^2+2ab+b^2 - a^2/b = (simplify a^2)
2ab+b^2/b = (cancel b's)
= 2a+b
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GMAT 1: 760 Q50 V44 Re: If f(a)=a2, what is the value of f(a+b)−f(a) b ? a b 2a 2a +  [#permalink]

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1
Bunuel wrote:
If f(a)=a^2, what is the value of (f(a+b)−f(a))/b ?

A. a
B. b
C. 2a
D. 2a + b
E. 2b - a

Kudos for correct solution.

f(a + b) = a^2 + b^ + 2ab
f(a) = a^2

f(a+b)−f(a) = a^2 + b^ + 2ab - a^2 = b^2 + 2ab

(f(a+b)−f(a))/b = b^2 + 2ab/b = b + 2a
Option D
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Re: If f(a)=a2, what is the value of f(a+b)−f(a) b ? a b 2a 2a +  [#permalink]

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Hello, can you clarify why f(a + b) = a^2 + b^ + 2ab?

Im missing the connection on how f(a) = a^2 relates to f(a + b) = a^2 + b^ + 2ab.

Thanks!
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Re: If f(a)=a2, what is the value of f(a+b)−f(a) b ? a b 2a 2a +  [#permalink]

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rodri102 wrote:
Hello, can you clarify why f(a + b) = a^2 + b^ + 2ab?

Im missing the connection on how f(a) = a^2 relates to f(a + b) = a^2 + b^ + 2ab.

Thanks!

rodri102, I'm over a year late to respond, but I see you are still an active user, so hopefully this is helpful.

The question tells us that the function If f(a)=$$a^2$$. This means that anything within the function is squared.

So f(a+b) = $$(a+b)^2$$

Now to work that out...

$$(a+b)^2$$ = (a+b)(a+b) = $$a^2 + ab + ab + b^2$$ = $$a^2 + 2ab + b^2$$

The question: What is the value of (f(a+b)−f(a))/b ?

$$\frac{a^2 + 2ab + b^2 - a^2}{b}$$

Cancel the $$a^2$$

$$\frac{2ab + b^2}{b}$$ = 2a+b
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