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For all real numbers x, the operation Δ is defined as xΔ = . If (bΔ)Δ

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For all real numbers x, the operation Δ is defined as xΔ = . If (bΔ)Δ [#permalink] New post   10 Jun 2016, 04:28
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For all real numbers x, the operation Δ is defined as xΔ =x+\(\frac{x}{4}\) . If (bΔ)Δ =\(\frac{25}{8}\) , what is the value of b ?

(A) 1.5

(B) 2

(C) 2.5

(D) 3

(E)3.5
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Re: For all real numbers x, the operation Δ is defined as xΔ = . If (bΔ)Δ [#permalink] New post   25 Nov 2018, 04:49
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Re: For all real numbers x, the operation Δ is defined as xΔ = . If (bΔ)Δ [#permalink] New post   10 Jun 2016, 04:41
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AbdurRakib wrote:
For all real numbers x, the operation Δ is defined as xΔ =x+\(\frac{x}{4}\) . If (bΔ)Δ =\(\frac{25}{8}\) , what is the value of b ?

(A) 1.5

(B) 2

(C) 2.5

(D) 3

(E)3.5



xΔ =x+\(\frac{x}{4} = \frac{5x}{4}\)...
so \((bΔ)Δ = \frac{5}{4}*\frac{5b}{4}\)=\(\frac{25}{8}\).................\(\frac{25b}{16}= \frac{25}{8}\)........b=2
B
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Re: For all real numbers x, the operation Δ is defined as xΔ = . If (bΔ)Δ [#permalink] New post   29 Sep 2018, 05:21
I somehow still struggle with this question a bit and had really on partly guessing to get it right.
Could someone provide a little more detailed approach to solving this question?

Thanks in advance!
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Re: For all real numbers x, the operation is defined as x = . If (b) [#permalink] New post   25 Jun 2023, 18:59
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AbdurRakib wrote:
For all real numbers x, the operation Δ is defined as xΔ =x+\(\frac{x}{4}\) . If (bΔ)Δ =\(\frac{25}{8}\) , what is the value of b ?

(A) 1.5
(B) 2
(C) 2.5
(D) 3
(E)3.5


If an operation is denoted with a strange symbol and defined through algebra, then this definition actually corresponds to a function:

x∆ = x + x/4 = 5x/4 is actually f(x) = x + x/4 = 5x/4

Let’s analyze the given situation:

(b∆)∆ = 25/8

(5b/4)∆ = 25/8

5(5b/4)/4 = 25/8

25b/16 = 25/8

b = 2

Answer: B
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Re: For all real numbers x, the operation is defined as x = . If (b) [#permalink]
25 Jun 2023, 18:59
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