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    I am stuck on the second part of this question. It's been bugging me for about an hour and I don't understand what it's asking me to do. Would really appreciate some help and pozzz rep in it.

    The even function f is defined over the domain -4>(or equal to) x (or equal to)< 4 by

    f(x)=x, 0<(or equal to) x <2

    f(x)= 4-x, 2>(or equal to) x (or equal to)< 4

    [a] Sketch the graph of f over its domain. GOT THIS.

    [b] Find all the values of x for which

    f(x)= (x+4)/4




    Thanks
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    (Original post by chussell)
    I am stuck on the second part of this question. It's been bugging me for about an hour and I don't understand what it's asking me to do. Would really appreciate some help and pozzz rep in it.

    The even function f is defined over the domain -4>(or equal to) x (or equal to)< 4 by

    f(x)=x, 0<(or equal to) x <2

    f(x)= 4-x, 2>(or equal to) x (or equal to)< 4

    [a] Sketch the graph of f over its domain. GOT THIS.

    [b] Find all the values of x for which

    f(x)= (x+4)/4

    Thanks

    Well, in the interval 0 to 2 for instance f(x) = x, therefore you are looking for solutions to x = (x+4)/4 which lie in that interval. If the solution doesn't lie in that interval then you're not interested in it.

    Similarly for the other intervals.

    Edit2: Remove alternate suggestion; nowt wrong with it, just not useful in this circumstance.
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    For (b) you need to consider the cases 0 \le x &lt; 2 and 2 \le x \le 4 separately.

    So you need to solve two equations: the first is x = \dfrac{x+4}{4} (and 0 \le x &lt; 2), and the second is 4-x = \dfrac{x+4}{4} (and 2 \le x \le 4). Remember in each case only to accept roots which are in the given ranges of x.
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    Thanks I seem to understand it a bit more now. However, this will seem very dumb, but what do you use as the values of x to plug in to the equations ? For some reason functions has me very, very confused.
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    (Original post by chussell)
    Thanks I seem to understand it a bit more now. However, this will seem very dumb, but what do you use as the values of x to plug in to the equations ? For some reason functions has me very, very confused.
    You don't plug in any values, you need to solve them.

    For example if you had x+3 = 5-x then you'd rearrange to get 2x=2 and so x=1... just solve the two equations, and make sure that the answer you get (e.g. 1 in my example) lies in the necessary range of values of x.
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    You sir, are a legend. Thanks a lot .
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    Hopefully you now have 4 solutions:
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