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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]  17 Feb 2017, 06:48
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Question Stats:

76% (02:21) correct 23% (01:33) wrong based on 26 sessions

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]  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]  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

[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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