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If f(x) = 2x^2 − 4 and g(x) = 2x, for what values of x will f(x) = g

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GeminiHeat
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If f(x) = 2x^2 − 4 and g(x) = 2x, for what values of x will f(x) = g [#permalink] New post   20 Feb 2021, 07:54
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If \(f(x) = 2x^2 − 4\) and \(g(x) = 2x\), for what values of x will \(f(x)= g(x)\)?

A. x = {1, 2}

B. x = {−1, 2}

C. x = {−1, −2}

D. x = {1, −2}

E. x = {−1, 1}
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B
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KarunMendiratta
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If f(x) = 2x^2 − 4 and g(x) = 2x, for what values of x will f(x) = g [#permalink] New post   20 Feb 2021, 07:59
GeminiHeat wrote:
If \(f(x) = 2x^2 − 4\) and \(g(x) = 2x\), for what values of x will \(f(x)= g(x)\)?

A. x = {1, 2}

B. x = {−1, 2}

C. x = {−1, −2}

D. x = {1, −2}

E. x = {−1, 1}


\(f(x) = g(x)\)
\(2x^2 − 4 = 2x\)
\(x^2 − 2 = x\)
\(x^2 − 2x - 4 = 0\)
\((x - 2)(x + 1) = 0\)
i.e. \(x = 2\) or \(-1\)

Hence, option B
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If f(x) = 2x^2 4 and g(x) = 2x, for what values of x will f(x) = g [#permalink] New post   03 Jul 2021, 03:46
Given that \(f(x) = 2x^2 − 4\) and \(g(x) = 2x\)

f(x) = g(x)
=> \(2x^2 − 4\) = 2x
=> \(2x^2\) - 2x - 4 = 0

Divide both the sides by 2 we get
=> \(x^2\) - x - 2 = 0
=> \(x^2\) + x - 2x - 2 = 0
=> x(x+1) - 2(x+1) = 0
=> (x+1) * (x-2) = 0
=> x = -1 or 2

So, Answer will be B
Hope it helps!

To learn more about Functions watch the following video

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If f(x) = 2x^2 4 and g(x) = 2x, for what values of x will f(x) = g [#permalink] New post   03 Sep 2023, 23:17
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\(f(x) = 2x^2 -4\)
\(g(x) = 2x\)

if \(f(x) = g(x)\), then

\(2x^2-4 = 2x\)

\(2x^2- 2x -4 = 0\)

dividing throughout by \(2\), we get

\(x^2 - x -2 = 0\)

\(x^2 -2x +x -2 = 0\)

\(x(x-2) +1(x-2) = 0\)

\((x+1)(x-2) = 0\)

For \(x = -1\) and \(x = 2\), \(f(x)=g(x)\).

The answer is Choice B.
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If f(x) = 2x^2 4 and g(x) = 2x, for what values of x will f(x) = g [#permalink]
03 Sep 2023, 23:17
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