Results 1 to 6 of 6

Math Help - f(x)=Cos(x) g(x)=Csc(x)Tan(x)

  1. #1
    Newbie
    Joined
    Jul 2010
    From
    California
    Posts
    13

    f(x)=Cos(x) g(x)=Csc(x)Tan(x)

    Use the given relations f and g to find (a) f g (b) f/g (f over g) (c) f∘g (d)g∘f
    f(x)=Cos(x) g(x)=Csc(x)Tan(x)

    can i see the steps on how to on these?
    Last edited by RosieLaird; July 20th 2010 at 04:46 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2008
    Posts
    2
    first you have to fine the domain for f(x),g(x).Then give a name for each (example:h=f*g,d=f/g,l= f∘g,k=g∘f)then find the domain for the new functions(this very important to do),and for the end right the type for the new functions!!ok?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    From
    California
    Posts
    13
    how do you find the domain and range for them?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member eumyang's Avatar
    Joined
    Jan 2010
    Posts
    278
    Thanks
    1
    I'll do (a)...
    \begin{aligned}<br />
f \cdot g &= (cos \, x)(csc \, x)(tan \, x) \\<br />
&= (cos \, x)\left( \frac{1}{sin \, x} \right) \left( \frac{sin \, x}{cos \, x} \right) \\<br />
&= 1<br />
\end{aligned}

    But this is not the same as your linear function y = 1. f \cdot g is going to look like a horizontal line with some "holes". The domain of f(x) = cos(x) is all real numbers, but the domain of g(x) = csc(x)tan(x) is all reals except multiples of pi/2. So the domain of f \cdot g is the intersection of the two domains, or all reals except multiples of pi/2.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2008
    Posts
    2
    for the f(x) we see cos which is real in real numbers so domain of f is R
    for g(x) it has y=css(x) wich means that the domain of that is R-{kπ},k in Z
    and u=tan(x) has domain R-{kπ+π/2}k in Z
    so domain for g(x) is R-{kπ+π/2,kπ},k in Z.ok now?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member Mathelogician's Avatar
    Joined
    Jun 2010
    From
    Iran
    Posts
    89
    Thanks
    1
    Quote Originally Posted by titos View Post
    for the f(x) we see cos which is real in real numbers so domain of f is R
    for g(x) it has y=csc(x) wich means that the domain of that isR-{kπ},k in Z
    and u=tan(x) has domain R-{kπ+π/2}k in Z
    so domain for g(x) is R-{kπ+-π/2,kπ},k in Z.ok now?
    That's Right!(Just do no forgot the -)
    Now as eumyang said, the intersection of domains of f and g is the domain of f.g
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum