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The function f is defined for all numbers x by f (x) = x2 +

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The function f is defined for all numbers x by f (x) = x2 + [#permalink] New post 17 Feb 2017, 06:48
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The function \(f\) is defined for all numbers \(x\) by \(f(x) = x^2 + x\). If t is a number such that \(f(2t) = 30\), which two of the following could be the number \(t\) ?

Indicate two such numbers.

❑ \(- 5\)

❑ \(- 3\)

❑ \(-\frac{1}{2}\)

❑ \(2\)

❑ \(\frac{5}{2}\)
[Reveal] Spoiler: OA

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Re: The function f is defined for all numbers x by f (x) = x2 + [#permalink] New post 27 Feb 2017, 16:00
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Explanation

Here we have the expression \(f(x)= x^2 + x\). This can be rewritten as \(f(x)= x(x+1)\). Now putting x = 2t in the expression we can rewrite the expression as:

\(f(2t)=2t(2t+1)\).

Our best strategy for this question is to put the option values and check if \(f(2t) = 30\).

❑ —5........... \(f(2*-5)= -10(-10+1) = -90\) NO

❑ —3........... \(f(2*-3)= -6(-6+1) = 30\) YES

❑ \(\frac{1}{2}\).......... \(f(2*\frac{1}{2})= 1(1+1) = 2\) No

❑ 2...........\(f(2*2)= 4(4+1) = 20\) NO

❑ \(\frac{5}{2}\).......... \(f(2*\frac{5}{2})= 5(5+1) = 30\) YES


Hence B and E are correct options.
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Re: The function f is defined for all numbers x by f (x) = x2 + [#permalink] New post 24 Mar 2017, 15:04
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Carcass wrote:


The function f is defined for all numbers x by f (x) = x² + x. If t is a number such that f (2t) = 30, which two of the following could be the number t ?

Indicate two such numbers.

❑ —5

❑ —3

❑ \(\frac{1}{2}\)

❑ 2

❑ \(\frac{5}{2}\)

[Reveal] Spoiler: OA
B and D


If f(x) = x² + x, then f(2t) = (2t)² + 2t
Since f(2t) = 30, we know that: (2t)² + 2t = 30
Simplify: 4t² + 2t = 30
Subtract 30 from both sides: 4t² + 2t - 30 = 0
Divide both sides by 2 to get: 2t² + t - 15 = 0
Factor to get: (2t - 5)(t + 3) = 0
So, EITHER 2t - 5 = 0 OR t + 3 = 0
If 2t - 5 = 0, then t = 5/2
If t + 3 = 0, then t = -3

Answer:
[Reveal] Spoiler:
B and E

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Re: The function f is defined for all numbers x by f (x) = x2 +   [#permalink] 24 Mar 2017, 15:04
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