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Thread: pre-Calculus HELP!

  1. #1
    tstaskal
    Guest

    Calculus HELP!

    Do not know what to do for the following:

    Find and simplify

    f(a+h) - f(a)

    for each function

    f(x) = 4 - x^2

    f(x) = x^2 +1
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  2. #2
    Super Member

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    Hello, tstaskal!

    Do you understand functional notation at all?

    Given a function $\displaystyle f(x)\!:\;f(a+h)$ means "replace each $\displaystyle x$ with $\displaystyle a+h$."


    Do not know what to do for the following:

    Find and simplify $\displaystyle f(a+h) - f(a)$ for each function:

    $\displaystyle (1)\;f(x) \,= \,4 - x^2$

    $\displaystyle (2)\;f(x)\,=\, x^2 +1$

    We are asked to find; .$\displaystyle f(a+h) - f(a)$

    Try to "read" what is says:
    . . (a) Find $\displaystyle f(a+h)$ . . . replace $\displaystyle x$ with $\displaystyle a+h$.
    . . (b) Then find $\displaystyle f(a)$ . . . replace $\displaystyle x$ with $\displaystyle a$.
    . . (c) Then subtract them: .$\displaystyle f(a+h) - f(a)$


    $\displaystyle (1)\;f(x)\:=\:4 - x^2$

    . . $\displaystyle (a)\;f(a+h) \;= \; 4 - (a+h)^2\;=\;4 - (a^2 + 2ah + h^2) \;=$ $\displaystyle \;4 - a^2 - 2ah - h^2$

    . . $\displaystyle (b)\;f(a)\;=\;4 - a^2$

    . . $\displaystyle (c)\;f(a+h) - f(a)\;=\;(4 - a^2 - 2ah - h^2) - (4 - a^2)
    \;= $ $\displaystyle 4 - a^2 - 2ah - h^2 - 4 + a^2$

    Answer: .$\displaystyle \boxed{-2ah - h^2}$


    You see? . . . It's just basic Algebra . . .

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