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If f(0.5) = 0, which of the following could be f(x)? (A) 2x

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Carcass
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If f(0.5) = 0, which of the following could be f(x)? (A) 2x [#permalink] New post   19 Jul 2019, 02:25
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If \(f(–0.5) = 0\), which of the following could be \(f(x)\)?

(A) \(2x + 2\)

(B) \(4x – 2\)

(C) \(4x^2 – 1\)

(D) \(x^2 – 1\)

(E) \((–x)^2 – 2.5\)
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C
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Re: If f(0.5) = 0, which of the following could be f(x)? (A) 2x [#permalink] New post   19 Jul 2019, 05:28
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Carcass wrote:
If \(f(–0.5) = 0\), which of the following could be \(f(x)\)?

(A) \(2x + 2\)

(B) \(4x – 2\)

(C) \(4x^2 – 1\)

(D) \(x^2 – 1\)

(E) \((–x)^2 – 2.5\)

With function problems and variables in the choices, plugging in values is the most efficient tactic.

In this case, plug (-0.5) into each choice to see if it = 0 to meet the conditions of the problem:

(A) 2(-0.5) + 2 ≠ 0 | Eliminate
(B) 4(-0.5) + 4 ≠ 0 | Eliminate
(C) 4(-0.5)² + 1 = 0 | Keep
(D) (-0.5)² + 1 ≠ 0 | Eliminate
(E) (0.5)² -2.5 ≠ 0 | Eliminate

Only one choice matches the conditions of the problem, so select Choice C.
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Re: If f(0.5) = 0, which of the following could be f(x)? (A) 2x [#permalink] New post   03 Dec 2024, 17:46
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\(f(–0.5) = 0\) and we need to find which of the following could be \(f(x)\)?

(A) \(2x + 2\)
x = -0.5
=> 2x + 2 = 2*-0.5 + 2 = 1 ≠ 0 => FALSE

(B) \(4x – 2\)
=> 4*(-0.5) -2 = -2 - 2 = -4 ≠ 0 => FALSE

(C) \(4x^2 – 1\)
=> 4*(-0.5)^2 - 1 = 1 - 1 = 0 => TRUE
We do not need to solve further but solving to complete the solution!

(D) \(x^2 – 1\)
=> \((-0.5)^2 - 1\) = 0.25 - 1 = -0.75 ≠ 0 => FALSE

(E) \((–x)^2 – 2.5\)
=> \((-(-0.5))^2 - 1\) = 0.25 - 1 = -0.75 ≠ 0 => FALSE

So, Answer will be C
Hope it helps!

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Re: If f(0.5) = 0, which of the following could be f(x)? (A) 2x [#permalink]
03 Dec 2024, 17:46
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