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Math Help - I need help with functions.

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    3

    I need help with functions.

    Can someone please help me solve these three problems:
    1) Let f be the function defined by f(x) = 2x^4 + 5. Find f(a+h), f(2a-h).

    2) Let f be the function defined by f(x) = -3x^2 – 3. Find f(1/2), f(-3/4).

    3) Let f(x) = 3x – 4 and g(x) = (-1/3)x^2 – 4x. Find f+g, f-g, f/g, f∙g, fg, gf.

    Thanks!!
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  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    1) As f(x)=2x^4+5,

    <br />
\begin{aligned}<br />
f(a+h)&=2(a+h)^4+5\\<br />
&=2(a^4+4a^3h+6a^2h^2+4ah^3+h^4)+5.<br />
\end{aligned}<br />

    f(a-h) can be found similarly.

    2) If f(x)=-3x^2-3, then f\left(\frac{1}{2}\right) and f\left(-\frac{3}{4}\right) can be found by evaluating

    -3\left(\frac{1}{2}\right)^2-3

    and

    -3\left(-\frac{3}{4}\right)^2-3.

    3) If f(x)=3x-4 and g(x)=-\frac{1}{3}x^2-4x, then

    <br />
\begin{aligned}<br />
(f+g)(x)&=(3x-4)+\left(-\frac{1}{3}x^2-4x\right)\\<br />
(f-g)(x)&=(3x-4)-\left(-\frac{1}{3}x^2-4x\right)\\<br />
(f/g)(x)&=\frac{3x-4}{\left(-\frac{1}{3}x^2-4x\right)}\\<br />
(f\cdot g)(x)&=(3x-4)\cdot\left(-\frac{1}{3}x^2-4x\right)\\<br />
\end{aligned}<br />
    <br />
\begin{aligned}<br />
(f\circ g)(x)&=\left(3\left(-\frac{1}{3}x^2-4x\right)-4\right).\\<br />
\end{aligned}<br />

    Hope this helps.
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