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

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New post 11 Aug 2015, 11:49
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If f(a)=\(a^{2}\), what is the value of \(\frac{f(a+b)−f(a)}{b}\)?



A) a

B) b

C) 2a

D) 2a + b

E) 2b - a

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

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New post 11 Aug 2015, 11:54
2
zxcvbnmas wrote:
If f(a)=\(a^{2}\), what is the value of \(\frac{f(a+b)−f(a)}{b}\)?



A) a

B) b

C) 2a

D) 2a + b

E) 2b - a



Method 1:

Given, \(f(a) = a^2\) ---> \(f(a+b) = (a+b)^2 = a^2+b^2+2ab\)

Thus \(\frac{f(a+b)−f(a)}{b}\) = \(\frac{a^2+b^2+2ab -a^2}{b}\) = 2a+b. D is the correct answer.

Method 2:

given : f(a) =\(a^2\) --> let a = 3---> f(3) = \(3^2\) = 9

let b = 3,

f(a+b) =f(3+3)=f(6)=36 and f(a) =9

Thus \(\frac{f(a+b)-f(a)}{b}\) = \(\frac{36-9}{3}\) = 9

Now see which option gives you 9 with a =b=3

A) a = 3. Eliminate

B) b = 3. Eliminate

C) 2a = 6. Eliminate

D) 2a + b = 9 . Correct

E) 2b - a = 3. Eliminate
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If f(a)=a^2, what is the value of (f(a+b)−f(a))/b ?  [#permalink]

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New post 11 Aug 2015, 13:02
given f(a) =a^2

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

f(a)=a^2

f(a+b)-f(a)/b= (a+b)^2-a^2/b=a^2+b^2+2ab-a^2/b=2a+b-- D is the answer


zxcvbnmas wrote:
If f(a)=\(a^{2}\), what is the value of \(\frac{f(a+b)−f(a)}{b}\)?



A) a

B) b

C) 2a

D) 2a + b

E) 2b - a

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

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New post 27 Jan 2017, 08:16
Engr2012 wrote:
zxcvbnmas wrote:
Method 1:

Given, \(f(a) = a^2\) ---> \(f(a+b) = (a+b)^2 = a^2+b^2+2ab\)

Thus \(\frac{f(a+b)−f(a)}{b}\) = \(\frac{a^2+b^2+2ab -a^2}{b}\) = 2a+b. D is the correct answer.

Method 2:

given : f(a) =\(a^2\) --> let a = 3---> f(3) = \(3^2\) = 9

let b = 3,

f(a+b) =f(3+3)=f(6)=36 and f(a) =9

Thus \(\frac{f(a+b)-f(a)}{b}\) = \(\frac{36-9}{3}\) = 9

Now see which option gives you 9 with a =b=3

A) a = 3. Eliminate

B) b = 3. Eliminate

C) 2a = 6. Eliminate

D) 2a + b = 9 . Correct

E) 2b - a = 3. Eliminate


In Method 1
\(f(a) = a^2\) ---> \(f(a+b) = (a+b)^2 = a^2+b^2+2ab\)
Is this a formula?Can anyone pls help.
How can I think If f(a) = a^2 then shift to f(a+b) = (a=b)^2????
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Re: If f(a)=a^2, what is the value of (f(a+b)−f(a))/b ?  [#permalink]

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New post 07 Aug 2017, 05:29
sunita123 wrote:
given f(a) =a^2

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

f(a)=a^2

f(a+b)-f(a)/b= (a+b)^2-a^2/b=a^2+b^2+2ab-a^2/b=2a+b-- D is the answer


zxcvbnmas wrote:
If f(a)=\(a^{2}\), what is the value of \(\frac{f(a+b)−f(a)}{b}\)?



A) a

B) b

C) 2a

D) 2a + b

E) 2b - a


Hey! I was concerned about the exact same problem. Do you already know why that's the case?
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Re: If f(a)=a^2, what is the value of (f(a+b)−f(a))/b ?  [#permalink]

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New post 10 Aug 2017, 10:32
zxcvbnmas wrote:
If f(a)=\(a^{2}\), what is the value of \(\frac{f(a+b)−f(a)}{b}\)?



A) a

B) b

C) 2a

D) 2a + b

E) 2b - a


Since f(a) = a^2, we can get the value of the given expression:

(f(a + b) - f(a))/b

(a^2 + 2ab + b^2 - a^2)/b

(2ab + b^2)/b

b(2a + b)/b = 2a + b

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

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New post 04 Dec 2017, 11:26
ENGRTOMBA2018 wrote:
zxcvbnmas wrote:
If f(a)=\(a^{2}\), what is the value of \(\frac{f(a+b)−f(a)}{b}\)?



A) a

B) b

C) 2a

D) 2a + b

E) 2b - a



Method 1:

Given, \(f(a) = a^2\) ---> \(f(a+b) = (a+b)^2 = a^2+b^2+2ab\)

Thus \(\frac{f(a+b)−f(a)}{b}\) = \(\frac{a^2+b^2+2ab -a^2}{b}\) = 2a+b. D is the correct answer.

Method 2:

given : f(a) =\(a^2\) --> let a = 3---> f(3) = \(3^2\) = 9

let b = 3,

f(a+b) =f(3+3)=f(6)=36 and f(a) =9

Thus \(\frac{f(a+b)-f(a)}{b}\) = \(\frac{36-9}{3}\) = 9

Now see which option gives you 9 with a =b=3

A) a = 3. Eliminate

B) b = 3. Eliminate

C) 2a = 6. Eliminate

D) 2a + b = 9 . Correct

E) 2b - a = 3. Eliminate


Hi,

In method 1, please elaborate as to how f(a + b) = (a + b)^2.

Thanks in advance.

Aiena.
Re: If f(a)=a^2, what is the value of (f(a+b)−f(a))/b ? &nbs [#permalink] 04 Dec 2017, 11:26
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