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Bunuel
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If f(a) = a^2, what is the value of (f(a + b) − f(a))/b ? 23 Dec 2019, 23:24
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D
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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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D
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uchihaitachi
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If f(a) = a^2, what is the value of (f(a + b) − f(a))/b ? 23 Dec 2019, 23:33
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\(f(a+b) = a^2 + b^2 + 2ab\)
\(f(a+b) - f(a) = a^2 + b^2 + 2ab - a^2 \) = \(b(b+2a)\)
\(\frac{f(a+b)−f(a)}{b}\) = \(\frac{b(b+2a)}{b}\) = b+2a

IMO, D

Bunuel
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 ? 24 Dec 2019, 02:26
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uchihaitachi
\(f(a+b) = a^2 + b^2 + 2ab\)
\(f(a+b) - f(a) = a^2 + b^2 + 2ab - a^2 \) = \(b(b+2a)\)
\(\frac{f(a+b)−f(a)}{b}\) = \(\frac{b(b+2a)}{b}\) = b+2a

IMO, D

Bunuel
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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Yes that's correct.

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If f(a) = a^2, what is the value of (f(a + b) − f(a))/b ? 24 Dec 2019, 02:55
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Given: \(f(a) = a^2, \)
Using above: \(f(a+b)=a^2+b^2+2ab\)

therefore \(\frac{(f(a + b) − f(a))}{b}\) = \(\frac{(a^2+b^2+2ab - a^2)}{b}\)

= \(\frac{(b^2+2ab)}{b}\) => \(b+2a\)

Option D
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If f(a) = a^2, what is the value of (f(a + b) − f(a))/b ? 11 Jan 2020, 06:44
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Can you please explain how you got f(a+b)=a^2+b^2+2ab
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If f(a) = a^2, what is the value of (f(a + b) − f(a))/b ? 11 Jan 2020, 07:08
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PalakDiwanji
Can you please explain how you got f(a+b)=a^2+b^2+2ab
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Given: \(f(a) = a^2, \)

In above(put 'a+b' in place of 'a'): \(f(a+b)\)= \( (a+b)^2\) => \(a^2+b^2+2ab\)

Hope it is clear!
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If f(a) = a^2, what is the value of (f(a + b) − f(a))/b ? 11 Jan 2020, 08:42
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got it now! Thanks a ton!

fauji
PalakDiwanji
Can you please explain how you got f(a+b)=a^2+b^2+2ab


Given: \(f(a) = a^2, \)

In above(put 'a+b' in place of 'a'): \(f(a+b)\)= \( (a+b)^2\) => \(a^2+b^2+2ab\)

Hope it is clear!
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If f(a) = a^2, what is the value of (f(a + b) − f(a))/b ? 08 Jan 2022, 05:21
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