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If f(z) = 2z+1, then which of the following can be the value of x for

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If f(z) = 2z+1, then which of the following can be the value of x for  [#permalink]

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New post Updated on: 29 May 2017, 11:04
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If \(f(z) = 2^{z+1}\), then which of the following can be the value of x for which \(f(1)∗f(2x)=f(x−1)∗(f(4)+f(−1))−f(1)\)?

A. -3

B. -2

C. \(−\frac{1}{8}\)

D. \(\frac{1}{8}\)

E. 4

Originally posted by niteshwaghray on 29 May 2017, 09:31.
Last edited by Bunuel on 29 May 2017, 11:04, edited 1 time in total.
Edited the question.
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Re: If f(z) = 2z+1, then which of the following can be the value of x for  [#permalink]

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New post 29 May 2017, 11:19
niteshwaghray wrote:
If \(f(z) = 2^{z+1}\), then which of the following can be the value of x for which \(f(1)∗f(2x)=f(x−1)∗(f(4)+f(−1))−f(1)\)?

A. -3

B. -2

C. \(−\frac{1}{8}\)

D. \(\frac{1}{8}\)

E. 4


\(f(1)∗f(2x)=f(x−1)∗(f(4)+f(−1))−f(1)\);

\(2^{(1+1)}∗2^{(2x+1)}=2^{(x-1+1)}∗(2^{(4+1)}+2^{(-1+1)})−2^{(1+1)}\);

\(2^{2}∗2^{(2x+1)}=2^{(x)}∗(2^{(5)}+2^{(0)})−2^{(2)}\);

\(2^2*2^{(2x)}*2=33*2^{(x)}−4\);

\(8*(2^x)^2 - 33*2^x + 4 = 0\).

Say 2^x = a, then \(8*a^2 - 33*a + 4 = 0\). Solve for a or factor to get \(a = 2^x = \frac{1}{8}\) or \(a = 2^x = 4\) --> \(x = -3\) or \(x = 2\).

Answer: A.

P.S. Not a fan of this question at all...
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Re: If f(z) = 2z+1, then which of the following can be the value of x for  [#permalink]

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New post 29 May 2017, 12:45
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This one can be solved by substitution method.

Use values from the answers.
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Re: If f(z) = 2z+1, then which of the following can be the value of x for  [#permalink]

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Re: If f(z) = 2z+1, then which of the following can be the value of x for   [#permalink] 02 Jan 2020, 09:14
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