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

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The function f has the property that f(x) = f(x + 1) [#permalink] New post 25 May 2016, 16:07
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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) ?

[Reveal] Spoiler: OA
17


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Re: The function f has the property that f(x) = f(x + 1) [#permalink] New post 26 May 2016, 04:49
f(x) = f(x + 1) and f (4) = 17 means this is a line y = 17, so f(8) will be 17 too
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Re: The function f has the property that f(x) = f(x + 1) [#permalink] New post 16 Oct 2017, 14:33
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Explanation

To get a feel for this information, let's first pick a random value for x.
Let's say x = 2
The given info tells us that f(x) = f(x + 1) for all values of x
So, f(2) = f(2 + 1)
In other words, f(2) = f(3)

Let's try a different value of x.
How about x = 3
The given info tells us that f(x) = f(x + 1) for all values of x
So, f(3) = f(3 + 1)
In other words, f(3) = f(4)

And so on.

We can see that f(2) = f(3) = f(4) = f(5) and so on
So, if f(4) = 17, we can be certain that f(8) = 17 as well.

Answer:
[Reveal] Spoiler:
17


Cheers,
Brent
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Re: The function f has the property that f(x) = f(x + 1) [#permalink] New post 10 Sep 2019, 09:21
Hi Brent, Sorry but I still didn't get why f(8) is same as f(4)?
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Re: The function f has the property that f(x) = f(x + 1) [#permalink] New post 10 Sep 2019, 15:38
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Salina wrote:
Hi Brent, Sorry but I still didn't get why f(8) is same as f(4)?


We're told that f(x) = f(x + 1)
So, f(4) = f(4 + 1)
In other words, f(4) = f(5)

Likewise, since f(x) = f(x + 1), we know that f(5) = f(5 + 1)
In other words, f(5) = f(6)

Keep going to see that f(4) = f(5) = f(6) = f(7) = f(8) = f(9) = ...etc

So, if f(4) = 17, then it is also true that f(5) = 17, f(6) = 17, f(7) = 17, f(8) = 17, f(9) = 17,...etc

Does that help?

Cheers,
Brent
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Re: The function f has the property that f(x) = f(x + 1)   [#permalink] 10 Sep 2019, 15:38
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