Question

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)?

Answer 1

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

Answer 2

um is it 6?

Answer 3

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 4

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

Answer 5

\[f(x) = f(x+1)\]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 \(x+1\)

Answer 6

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

Answer 7

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

Answer 8

yes

Answer 9

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

Answer 10

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

Answer 11

yes

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

okay yes

Answer 17

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

Answer 18

yes

Answer 19

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

Answer 20

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

Answer 21

yes it is tricky

Answer 22

yomamafb u r forgetting somthing

Answer 23

?

Answer 24

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

Answer 25

u were going to tell a number

Answer 26

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

Answer 27

fml

Answer 28

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

Answer 29

it was a trick question everything equals 17