Results 1 to 2 of 2

Thread: 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!!
    Follow Math Help Forum on Facebook and Google+

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

    $\displaystyle
    \begin{aligned}
    f(a+h)&=2(a+h)^4+5\\
    &=2(a^4+4a^3h+6a^2h^2+4ah^3+h^4)+5.
    \end{aligned}
    $

    $\displaystyle f(a-h)$ can be found similarly.

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

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

    and

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

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

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

    Hope this helps.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: Apr 15th 2010, 05:50 PM
  2. Replies: 3
    Last Post: Feb 23rd 2010, 04:54 PM
  3. Replies: 11
    Last Post: Nov 15th 2009, 11:22 AM
  4. Replies: 7
    Last Post: Aug 12th 2009, 04:41 PM
  5. Replies: 1
    Last Post: Apr 15th 2008, 09:00 AM

Search Tags


/mathhelpforum @mathhelpforum