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anonymous

  • one year ago

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)?

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  1. whpalmer4
    • one year ago
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    If we know that \(f(x) = f(x+1)\) for all values of \(x\), then if we know \(f(4)=17\), what does \(f(5)=\)

  2. anonymous
    • one year ago
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    um is it 6?

  3. imqwerty
    • one year ago
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    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.

  4. anonymous
    • one year ago
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    wait why is f(8)=17? I'm so confused ....

  5. whpalmer4
    • one year ago
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    \[f(x) = f(x+1)\]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 \(x+1\)

  6. anonymous
    • one year ago
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    yes i understand that but y is f(8)=17?

  7. whpalmer4
    • one year ago
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    we know that \(f(4) = 17\) right?

  8. anonymous
    • one year ago
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    yes

  9. imqwerty
    • one year ago
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    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

  10. whpalmer4
    • one year ago
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    okay, and we know that whatever value \(f(x)\) has, \(f(x+1)\) has the same value

  11. anonymous
    • one year ago
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    yes

  12. whpalmer4
    • one year ago
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    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

  13. anonymous
    • one year ago
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    wait what? why is f(5)=17 now?

  14. whpalmer4
    • one year ago
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    for any value of \(x\), pick a number, any number, \(f(x) = f(x+1)\) or \(f(x+1) = f(x)\)

  15. whpalmer4
    • one year ago
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    the problem tells us that..."for all numbers x"...

  16. anonymous
    • one year ago
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    okay yes

  17. whpalmer4
    • one year ago
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    okay, so if \{f(4) = 17\), then we are taking \(x = 4\) and we can write \(f(4) = f(4+1) = 17\) because \(f(x) = f(x+1)\)

  18. anonymous
    • one year ago
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    yes

  19. whpalmer4
    • one year ago
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    okay, if f(5) = 17, what does f(6)? remember, 5+1 = 6

  20. anonymous
    • one year ago
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    wait.... so this is a trick question? everything equals to 17?

  21. imqwerty
    • one year ago
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    yes it is tricky

  22. imqwerty
    • one year ago
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    yomamafb u r forgetting somthing

  23. anonymous
    • one year ago
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    ?

  24. anonymous
    • one year ago
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    oh i just saw your reply ..... so EVERYTHING equals to 17? wth so this was a trick question!

  25. imqwerty
    • one year ago
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    u were going to tell a number

  26. whpalmer4
    • one year ago
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    yes, exactly, in this case, the value of \(f(x) = 17\) for every value of \(x\)

  27. anonymous
    • one year ago
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    fml

  28. Hero
    • one year ago
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    f(2) = f(3) f(3) = f(4) f(4) = f(5) ...

  29. anonymous
    • one year ago
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    it was a trick question everything equals 17

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