Results 1 to 11 of 11
Like Tree1Thanks
  • 1 Post By Soroban

Math Help - Formula for f of g

  1. #1
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Formula for f of g

    Formula for f of g-more-logs.jpgClick the image to enlarge please.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,709
    Thanks
    1639
    Awards
    1

    Re: Formula for f of g

    Quote Originally Posted by Eraser147 View Post
    Click image for larger version. 

Name:	More logs.JPG 
Views:	15 
Size:	14.5 KB 
ID:	25132Click the image to enlarge please.
    f\circ g(x)=7^{2+5\log_7(x)}

    BUT that can be greatly simplified.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Re: Formula for f of g

    Yes, but going from there, I don't know how to find the x. It's just too confusing from there. I don't know which exponent I can factor out.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member alane1994's Avatar
    Joined
    Oct 2012
    From
    Iowa, United States
    Posts
    65
    Thanks
    8

    Re: Formula for f of g

    Plato is correct. If you want f of g, you just plug the g function into the x spot on the f function.
    f=number^x
    g=blahx
    then f\circ g(x)=number^{blahx}
    Does this make sense?
    If I am incorrect on this please correct me!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,709
    Thanks
    1639
    Awards
    1

    Re: Formula for f of g

    Quote Originally Posted by Eraser147 View Post
    Yes, but going from there, I don't know how to find the x. It's just too confusing from there. I don't know which exponent I can factor out.
    Well I did say "that can be greatly simplified."

    f\circ g(x)=7^{2+5\log_7(x)}=49x^5
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,749
    Thanks
    650

    Re: Formula for f of g

    Hello, Eraser147!

    \text{Given: }\begin{Bmatrix}f(x) &=& 7^{2+5x} \\ g(x) &=& \log_7(x) \end{Bmatrix} \quad \text{ Find }f\!\!\circ\! g.

    f\!\!\circ\!g \;=\;f(g(x))

    . . . =\;f(\log_7x)

    . . . =\;7^{2+5\log_7(x)}

    . . . =\;7^2\cdot 7^{5\log_7(x)}

    . . . =\;49\cdot 7^{\log_7(x^5)}

    . . . =\;49\cdot x^5

    . . . =\;49x^5
    Thanks from Eraser147
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Re: Formula for f of g

    ^ Thankyou that made more sense. I had to separate the 7s.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Re: Formula for f of g

    Just one more question, can someone explain why when 7 is extended to the power of log 7 and raised to the x^5, why does it cancel and equate to x^5?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,709
    Thanks
    1639
    Awards
    1

    Re: Formula for f of g

    Quote Originally Posted by Eraser147 View Post
    Just one more question, can someone explain why when 7 is extended to the power of log 7 and raised to the x^5, why does it cancel and equate to x^5?
    b^{\log_b(a)}=a~\&~b^{n\log_b(a)}=b^{\log_b(a^n)}=  a^n
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Member
    Joined
    Oct 2012
    From
    Nowhere
    Posts
    82

    Re: Formula for f of g

    Thanks
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,791
    Thanks
    1531

    Re: Formula for f of g

    That is, pretty much, the definition of " log_a(x)"- it is the inverse function to a^x: a^{log_a(x)}= log_a(a^x)= x.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stupid formula, I get the question but not the formula
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: August 15th 2012, 01:23 PM
  2. Replies: 0
    Last Post: August 1st 2012, 11:06 AM
  3. Replies: 4
    Last Post: July 15th 2011, 01:30 PM
  4. Replies: 8
    Last Post: September 5th 2010, 12:11 PM
  5. Replies: 1
    Last Post: April 26th 2010, 07:16 PM

Search Tags


/mathhelpforum @mathhelpforum