Results 1 to 7 of 7

Math Help - Interesting Question

  1. #1
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599

    Interesting Question

    This is from a Mu Alpha Theta Competition I took today.

    19. Let f and g be functions such that f(x)^2=g^{-1}(4x-1). What is f(x)f'(x)g'(f(x)^2)?

    A) Not enough information
    B)2
    C) \frac{2}{4x-1}
    D)8x-2


    I didn't really know how to approach this, so a little push would be great.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Jameson
    This is from a Mu Alpha Theta Competition I took today.

    19. Let f and g be functions such that f(x)^2=g^{-1}(4x-1). What is f(x)f'(x)g'(f(x)^2)?

    A) Not enough information
    B)2
    C) \frac{2}{4x-1}
    D)8x-2


    I didn't really know how to approach this, so a little push would be great.
    <br />
f(x)^2=g^{-1}(4x-1)<br />

    Rewrite as:

    <br />
g([f(x)]^2)=4x-1<br />

    Now differentiate wrt x.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by CaptainBlack
    <br />
f(x)^2=g^{-1}(4x-1)<br />

    Rewrite as:

    <br />
g([f(x)]^2)=4x-1<br />

    Now differentiate wrt x.

    RonL
    How do you know it is differenciable
    Last edited by ThePerfectHacker; March 4th 2006 at 03:14 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ThePerfectHacker
    How do you know it is differenciable
    1. It is a linear form in x and so differentiable wrt x.

    2. If f and g are differentiable then this is differentiable. Asking the
    question implies we may assume that f and g are differentiable, just
    as it allows us to assume that ' denotes the derivative.


    RonL
    Last edited by CaptainBlack; March 5th 2006 at 09:39 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    I was making a remark that in analysis you always need to show diffrenciability before taking the derivative, I just found that funny.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Quote Originally Posted by CaptainBlack
    <br />
f(x)^2=g^{-1}(4x-1)<br />

    Rewrite as:

    <br />
g([f(x)]^2)=4x-1<br />

    Now differentiate wrt x.

    RonL
    So I get that g'[f(x)^2]*2f(x)*f'(x)=4, so my answer is 2.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Jameson
    So I get that g'[f(x)^2]*2f(x)*f'(x)=4, so my answer is 2.
    That's what I get

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. interesting question
    Posted in the Business Math Forum
    Replies: 1
    Last Post: September 30th 2010, 11:26 PM
  2. Interesting Question...
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 23rd 2010, 05:23 PM
  3. interesting question
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 8th 2010, 12:41 PM
  4. Interesting question ?....
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 4th 2009, 10:57 AM
  5. interesting question
    Posted in the Advanced Applied Math Forum
    Replies: 7
    Last Post: October 11th 2007, 09:48 PM

Search Tags


/mathhelpforum @mathhelpforum