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Math Help - Composite function

  1. #1
    Senior Member DivideBy0's Avatar
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    Composite function

    If f(x)=\frac{1}{x-1} for x>2 and f(x)=x+1 for 2 \geq x, find f(a-2) in terms of a.

    Normally I would simply substitute a in, but I don't know if that is the right way to go about things?

    I think I should have considered pre-calc a little more carefully before going into calc
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by DivideBy0 View Post
    If f(x)=\frac{1}{x-1} for x>2 and f(x)=x+1 for 2 \geq x, find f(a-2) in terms of a.

    Normally I would simply substitute a in, but I don't know if that is the right way to go about things?...
    Hello,

    of course your plan is OK - but you have to plug in the term (a-2) into the conditions too:

    f(x)=\left \{\begin{array}{lr}\frac{1}{x-1}  & x>2 \\x+1 & x\leq 2\end{array}\right.

    Now you get:

    f(a-2)=\left \{\begin{array}{lr}\frac{1}{a-2-1}  & a-2>2 \\a-2+1 & a-2\leq 2\end{array}\right. After simplifying a little bit you have:

    f(a-2)=\left \{\begin{array}{lr}\frac{1}{a-3}  & a>4 \\a-1 & a\leq 4 \end{array}\right.
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