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GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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If f(x) = x2, which of the following is equal to f(m + n) + [#permalink]
Expert's post 00:00

Question Stats: 80% (00:31) correct 19% (00:33) wrong based on 21 sessions
If $$f(x) = x^2$$, which of the following is equal to $$f(m + n) + f(m - n)$$?

(A) $$m^2 + n^2$$
(B) $$m^2 - n^2$$
(C) $$2m^2 + 2n^2$$
(D) $$2m^2 - 2n^2$$
(E) $$m^2n^2$$
[Reveal] Spoiler: OA

_________________

Sandy
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Intern Joined: 10 Aug 2018
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Re: If f(x) = x2, which of the following is equal to f(m + n) + [#permalink]
It will save a lot of time for many problems if you keep in mind that (m+n)^2 = m^2+n^2+2mn and (m-n)^2 = m^2+n^2-2mn. Here it obviously gives you the answer:

f(m+n)+f(m-n)= m^2 + n^2 + 2mn + m^2 + n^2 - 2mn = 2m^2 + 2n^2

So C

But this also comes in handy when it comes to remembering the inequality:

m^2 + n^2 <= (m+n)^2
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 , given: 397

Re: If f(x) = x2, which of the following is equal to f(m + n) + [#permalink]
Expert's post
Explanation

The problem provides the function $$f(x) = x^2$$ and asks for the quantity $$f(m + n) + f(m - n)$$.

Plug into this function twice—first, to insert m + n in place of x, and then to insert $$m - n$$ in place of x:

$$f(m + n) = (m + n)^2 = m^2 + 2mn + n^2$$

$$f(m - n) = (m - n)2 = m^2 - 2mn + n^2$$

Now add the two:

$$(m^2 + 2mn + n^2) + (m^2 - 2mn + n^2) = 2m^2 + 2n^2$$
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Sandy
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Director Joined: 09 Nov 2018
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Re: If f(x) = x2, which of the following is equal to f(m + n) + [#permalink]
Romang67 wrote:
It will save a lot of time for many problems if you keep in mind that (m+n)^2 = m^2+n^2+2mn and (m-n)^2 = m^2+n^2-2mn. Here it obviously gives you the answer:

f(m+n)+f(m-n)= m^2 + n^2 + 2mn + m^2 + n^2 - 2mn = 2m^2 + 2n^2

So C

But this also comes in handy when it comes to remembering the inequality:

m^2 + n^2 <= (m+n)^2

Is it m^2 + n^2 <= (m+n)^2
or
m^2 + n^2 < (m+n)^2 (Without = sign).
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 , given: 397

Re: If f(x) = x2, which of the following is equal to f(m + n) + [#permalink]
Expert's post
AE wrote:

Is it m^2 + n^2 <= (m+n)^2
or
m^2 + n^2 < (m+n)^2 (Without = sign).

If m and n are positive or both strictly negative (i.e non 0). Then:

$$m^2 + n^2 < (m+n)^2$$ because $$(m+n)^2= m^2 + n^2 + 2mn$$ now $$2mn$$ is positive for m and n being positive.

For $$m=n=0$$ they are equal.

If m and n have different signs then the inequality flips and $$m^2+n^2 > (m+n)^2$$.
_________________

Sandy
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Try our free Online GRE Test Re: If f(x) = x2, which of the following is equal to f(m + n) +   [#permalink] 19 Nov 2018, 13:26
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