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If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the

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If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the  [#permalink]

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26 May 2020, 01:42
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If $$\frac{f(x)}{f(x−1)} = \frac{(x−2)}{(x+1)}$$, for all $$x ≥ 0$$ and $$f(6) = 81$$, what is the value of $$f(4)$$?

A. 282
B. 282.5
C. 283
D. 283.5
E. 284

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Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the  [#permalink]

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26 May 2020, 02:03
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See the attachment -> D
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Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the  [#permalink]

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26 May 2020, 02:32
1
F{x}/F{x-1} = (X-2)/(X+1) -----(1)
PUT F(X) = F(6) = 81
F(6)/F(5)= 4/7
F(5) = 81*7/4
F(5) = 567/4 -----(2)

PUT F(5) VALUE IN THE EQUATION (1)
F(5)/F(4) = 3/6
(567/4)/F(4) = 1/2
F(4) = 567*2/4
F(4) = 567/2 => 283.5

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Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the  [#permalink]

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26 May 2020, 03:09
1
Bunuel wrote:
If $$\frac{f(x)}{f(x−1)} = \frac{(x−2)}{(x+1)}$$, for all $$x ≥ 0$$ and $$f(6) = 81$$, what is the value of $$f(4)$$?

A. 282
B. 282.5
C. 283
D. 283.5
E. 284

Solution

• We have $$\frac{f(x)}{f(x-1)} = \frac{(x – 2)}{(x+1)}$$
Substituting x = 6 in the above equation, we get,
• $$\frac{f(6)}{f(5)} =\frac{4}{7} …………..Eq.(i)$$
Substituting x = 5 in the the given expression, we get,
• $$\frac{f(5)}{f(4)} =\frac{3}{6} …………..Eq.(ii)$$
Now, from Eq.(i) and Eq.(ii), we can write,
• $$\frac{f(6)}{f(5)}* \frac{f(5)}{f(4)} =\frac{4}{7}*\frac{3}{6}$$
$$⟹\frac{f(6)}{f(4)} = \frac{2}{7}$$
$$⟹f(4) = f(6)* \frac{7}{2} = 81*\frac{7}{2} =283.5$$
Thus, the correct answer is Option D.
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Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the  [#permalink]

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26 May 2020, 08:07
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If f(x)/f(x−1)=(x−2)/(x+1), for all x≥0x≥0 and f(6)=81, what is the value of f(4)?

A. 282
B. 282.5
C. 283
D. 283.5
E. 284

f(6)/f(5) = 4/7

similarly, f(5)/f(4) = 3/6 = 1/2

Multiplying both, f(6)/f(4) = 2/7 => f(4) = 7 * 81/2 = 283.5

So D
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Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the  [#permalink]

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30 May 2020, 13:33
Bunuel wrote:
If $$\frac{f(x)}{f(x−1)} = \frac{(x−2)}{(x+1)}$$, for all $$x ≥ 0$$ and $$f(6) = 81$$, what is the value of $$f(4)$$?

A. 282
B. 282.5
C. 283
D. 283.5
E. 284

First, letting x = 6, we have:

f(6)/f(5) = 4/7

81/f(5) = 4/7

4 * f(5) = 567

f(5) = 567/4

Now, letting x = 5, we have:

f(5)/f(4) = 3/6

(567/4)/f(4) = 1/2

f(4) = 2 * 567/4

f(4) = 567/2 = 283.5

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Re: If f(x)/f(x−1) = (x−2)/(x+1), for all x ≥ 0 and f(6) = 81, what is the   [#permalink] 30 May 2020, 13:33