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The function f has the property that f(x) = f(x + 1) for all numbers x

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Bunuel
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The function f has the property that f(x) = f(x + 1) for all numbers x [#permalink] New post   06 Dec 2018, 04:52
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The function f has the property that f(x) = f(x + 1) for all numbers x. If f(4) = 17, what is the value of f(8) ?

A. 11
B. 13
C. 15
D. 17
E. 18
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BrentGMATPrepNow
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Re: The function f has the property that f(x) = f(x + 1) for all numbers x [#permalink] New post   06 Dec 2018, 08:32
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Bunuel wrote:
The function f has the property that f(x) = f(x + 1) for all numbers x. If f(4) = 17, what is the value of f(8) ?

A. 11
B. 13
C. 15
D. 17
E. 18


Let's get a better understanding of what it means to say that f(x) = f(x + 1) for all numbers x

So, if x = 2, then we can say that f(2) = f(2 + 1)
In other words, f(2) = f(3)

Likewise, if x = 7, then we can say that f(7) = f(7 + 1)
In other words, f(7) = f(8)

We told that f(4) = 17
The given rule tells us that f(4) = f(4 +1) = f(5)
So, if f(4) = 17, then it's also true that f(5) = 17

Of course, if f(5) = 17, then f(5 + 1) = 17 as well (based on the given rule)
In other words, f(6) = 17

Applying the given rule, we can conclude that f(4) = f(5) = f(6) = f(7) = f(8) = f(9) = f(10) = . . .
So, if f(4) = 17, then it must be the case that f(8) = 17

Answer: D

Cheers,
Brent
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Re: The function f has the property that f(x) = f(x + 1) for all numbers x [#permalink] New post   06 Dec 2018, 10:17
F(x) = F(x+1)
F(4) = 17
F(8) = ?

F(4) = F(4+1) = F(5) = 17
F(4) = F(5)

F(5)=17
F(5) = F(5+1) = F(6) = 17
F(5)=F(6)

F(6) = F(6+1) = F(7) = 17
F(6) = F(7)

F(7) = F(7+1) = F(8) = 17
F(7) = F(8)

So F(8) = 17
IMO D
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Re: The function f has the property that f(x) = f(x + 1) for all numbers x [#permalink] New post   05 Nov 2020, 13:11
Expert Reply
Bunuel wrote:
The function f has the property that f(x) = f(x + 1) for all numbers x. If f(4) = 17, what is the value of f(8) ?

A. 11
B. 13
C. 15
D. 17
E. 18


Solution:

We are given that f(x) = f(x + 1). This means, for example, that f(2) = f(2 + 1), which means that f(2) = f(3) and f(3) = f(3 + 1) = f(4). We can extend this to f(2) = f(3) = f(4) = f(5), and so on. Thus, the function is actually a constant function. Therefore, if we know that f(4) = 17, then f(any number) = 17, and so f(8) = 17.

Answer: D
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Re: The function f has the property that f(x) = f(x + 1) for all numbers x [#permalink] New post   05 Nov 2020, 13:43
We are given that:
f(x) = f(x+1)

Hence f(1) = f(1+1) = f(2)
Similarly f(2) = f(3)
And f(3) = f (4) = f(5).... =f(8)

Basically the function yields same result for all variables x.

Hence f(8) = f (4) = 17

ie Option D

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Re: The function f has the property that f(x) = f(x + 1) for all numbers x [#permalink] New post   08 Dec 2020, 23:25
Given: The function f has the property that f(x) = f(x + 1) for all numbers x.
Asked: If f(4) = 17, what is the value of f(8) ?

f(4) = f(5) = f(6) = f(7) = f(8) = 17

IMO D
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Re: The function f has the property that f(x) = f(x + 1) for all numbers x [#permalink] New post   09 Dec 2020, 00:45
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f(x) = f(x + 1)

f(4) = f(4 + 1) = f(5) = f(6) = f(7) = f(8) = 17

Answer D
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Re: The function f has the property that f(x) = f(x + 1) for all numbers x [#permalink] New post   10 Jul 2023, 10:53
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Re: The function f has the property that f(x) = f(x + 1) for all numbers x [#permalink]
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