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)?

- anonymous

- chestercat

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- whpalmer4

If we know that \(f(x) = f(x+1)\) for all values of \(x\), then if we know \(f(4)=17\), what does \(f(5)=\)

- anonymous

um is it 6?

- imqwerty

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.

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## More answers

- anonymous

wait why is f(8)=17? I'm so confused ....

- whpalmer4

\[f(x) = f(x+1)\]is just a way of saying that whatever the value of the function \(f(x)\) is at some value of \(x\), it has the same value at \(x+1\)

- anonymous

yes i understand that but y is f(8)=17?

- whpalmer4

we know that \(f(4) = 17\) right?

- anonymous

yes

- imqwerty

Another approach is to create some kind of function that satisfies the condition that f(x) = f(x + 1) for all values of x, AND also f(4) = 17
Here's one:
f(x) = (x)(0) + 17
Here we can see that:
f(1) = 17
f(2) = 17
f(2) = 17
f(3) = 17
f(4) = 17
.
.
.
f(8) = 17

- whpalmer4

okay, and we know that whatever value \(f(x)\) has, \(f(x+1)\) has the same value

- anonymous

yes

- whpalmer4

so that means that \(f(4) = f(4+1) = f(5)\) and we already know that \(f(4) = 17\) so that means \(f(5) = 17\) as well

- anonymous

wait what? why is f(5)=17 now?

- whpalmer4

for any value of \(x\), pick a number, any number, \(f(x) = f(x+1)\) or \(f(x+1) = f(x)\)

- whpalmer4

the problem tells us that..."for all numbers x"...

- anonymous

okay yes

- whpalmer4

okay, so if \{f(4) = 17\), then we are taking \(x = 4\) and we can write \(f(4) = f(4+1) = 17\)
because \(f(x) = f(x+1)\)

- anonymous

yes

- whpalmer4

okay, if f(5) = 17, what does f(6)?
remember, 5+1 = 6

- anonymous

wait.... so this is a trick question? everything equals to 17?

- imqwerty

yes it is tricky

- imqwerty

yomamafb u r forgetting somthing

- anonymous

?

- anonymous

oh i just saw your reply ..... so EVERYTHING equals to 17? wth so this was a trick question!

- imqwerty

u were going to tell a number

- whpalmer4

yes, exactly, in this case, the value of \(f(x) = 17\) for every value of \(x\)

- anonymous

fml

- Hero

f(2) = f(3)
f(3) = f(4)
f(4) = f(5)
...

- anonymous

it was a trick question everything equals 17

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