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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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Joined: 14 Sep 2015
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Location: India
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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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Updated on: 29 May 2017, 11:04
13
00:00

Difficulty:

95% (hard)

Question Stats:

38% (03:07) correct 63% (03:28) wrong based on 98 sessions

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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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Joined: 02 Sep 2009
Posts: 51218
Re: If f(z) = 2z+1, then which of the following can be the value of x for  [#permalink]

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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 $$x = 2$$.

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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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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05 Jul 2018, 07:57
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Re: If f(z) = 2z+1, then which of the following can be the value of x for &nbs [#permalink] 05 Jul 2018, 07:57
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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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