Results 1 to 3 of 3

Math Help - Functions Help.

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    22

    Functions Help.

    Hii (: I spend a couple of hours on these problems and I don't know how to solve them:

    1. Show that if f is a constant function and g is any fucntion, then f of g and g of f are both constant functions.

    2. Give an example of three functions f, g and h, none of which is a constant function, such that f of g = f of h but g is not equal to h.

    I'm not sure if this is right but i did..
    h(x)= x^2 , g(x)= x-3, and f(x)= √x
    does that work? D:

    3. Suppose f is a function whose domain equals to {2,4,7,8,9} and whose range equals to {-3,0,2,6,7}. Explain why f is a one to one function.

    I don't understand what they mean by one to one function and the {2,4,7,8,9} thing. What does does it mean?

    4. Give an example of a function f such that the domain of f and the range of f both equal the set of integers, but f is not a one to one function.


    5. Explain why an even function whose domain contains a nonzero number cannot be a one-to-one function.



    Thank you in advancee (: (: <3
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by TeriyakiDonnQ View Post
    1. Show that if f is a constant function and g is any fucntion, then f of g and g of f are both constant functions.

    For example, if:

    f:A\rightarrow B\;,g:B\rightarrow C\;,\;\quad f(x)=k\;(\forall x\in A)

    then

    (g\circ f)(x)=g[f(x)]=f(k)\quad (\forall x\in A)

    that is, g\circ f is constant.


    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by TeriyakiDonnQ View Post
    Hii (: I spend a couple of hours on these problems and I don't know how to solve them:

    1. Show that if f is a constant function and g is any fucntion, then f of g and g of f are both constant functions.

    2. Give an example of three functions f, g and h, none of which is a constant function, such that f of g = f of h but g is not equal to h.

    I'm not sure if this is right but i did..
    h(x)= x^2 , g(x)= x-3, and f(x)= √x
    does that work? D:

    3. Suppose f is a function whose domain equals to {2,4,7,8,9} and whose range equals to {-3,0,2,6,7}. Explain why f is a one to one function.

    I don't understand what they mean by one to one function and the {2,4,7,8,9} thing. What does does it mean?

    4. Give an example of a function f such that the domain of f and the range of f both equal the set of integers, but f is not a one to one function.


    5. Explain why an even function whose domain contains a nonzero number cannot be a one-to-one function.



    Thank you in advancee (: (: <3
    Please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. See rule #8: http://www.mathhelpforum.com/math-he...ng-151418.html.

    Thread closed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 15th 2010, 06:50 PM
  2. Replies: 3
    Last Post: February 23rd 2010, 05:54 PM
  3. Replies: 11
    Last Post: November 15th 2009, 12:22 PM
  4. Replies: 7
    Last Post: August 12th 2009, 05:41 PM
  5. Replies: 1
    Last Post: April 15th 2008, 10:00 AM

Search Tags


/mathhelpforum @mathhelpforum