1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

F(x), G(x) Etc

  1. Oct 23, 2004 #1
    Dear friends,


    please can you help me to understand what f(x) means?

    I am just starting out at high school maths level.....

    In a book it also says g(x) h(x) etc what does it mean ??

    Also does the x in the brackets ever change and if so what does it mean ?


    Thankyou for any advice.


    Roger
     
  2. jcsd
  3. Oct 23, 2004 #2

    dav2008

    User Avatar
    Gold Member

    f(x) and g(x) (or any other letter) are notations for functions.

    f(x) is read as "eff of x".

    let's say that f(x) = x+3.

    that means there is a function of x that takes the input and adds 3 to it, so f(3) =3+3.

    the f or g or h are just standard letters for representing functions.

    You can have
    f(x) = x2
    g(x) = x-2

    So if you want to find f(3) it would be 32=9.
    g(3) would be 3-2=1

    Edit: Typo, put a 3 instead of 2
     
    Last edited: Oct 23, 2004
  4. Oct 23, 2004 #3

    brewnog

    User Avatar
    Science Advisor
    Gold Member

    ^ what he said.

    And also, for all intents and purposes:

    f(x) = 3x

    means *basically* the same thing as:

    y = 3x

    as you may already be familiar with this notation.
     
  5. Oct 23, 2004 #4

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Ugh, don't say that. :cry: It might help him for a little while, but can only lead to confusion later.
     
  6. Oct 23, 2004 #5

    cepheid

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Why? Do you mean because it's only true if y = f(x)? i.e. that y and f(x) could be totally different things? Or is there some other more fundamental difference between a dependent variable (whose dependence can be described as a functional relationship) and a function itself that I should have picked up on a long time ago?
     
  7. Oct 24, 2004 #6

    brewnog

    User Avatar
    Science Advisor
    Gold Member

    I'm sorry. With all due respect to roger, the questions he's asking are at a pretty fundamental level (relative to a lot of the stuff on this forum in any case), and I thought that my simple (if not entirely accurate) analogy might serve him well, if only for the time being. I remember clearly being taught this new notation years back, and I definitely thought of it this way until I got my head round it all. It's also the reason I put "basically" in nice sparkly asterisks :)

    Sorry for any confusion roger!
     
  8. Oct 24, 2004 #7

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Sometimes using "shortcuts" does help, but you always have to remember their dangers: it may stifle one's ability to use the thing without the shortcut, or worse believe the thing is the shortcut.


    I guess the reason for my reaction is that the biggest problem I've seen happen is understanding evaluation: they could tell you what f(x) is, or f(4), maybe what f(t) is, but be entirely stumped by f(x+1). Because evaluation is central to the concept of a function, I would be very hesitant to suggest anything that obscures it.
     
  9. Oct 24, 2004 #8

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Strictly speaking, if "f" is a function, then "f(x)" is the (numerical) value when f is applied to the value x.
     
  10. Oct 24, 2004 #9
    Dear HallsofIvy,

    what if the equation is 3x^2 + 5x +9 = Y

    and It says f(x+3)

    Does it mean replace all of the x in the equation by x+3 ?

    I'm trying to understand the difference between af(x) and f(ax) ?


    Thankyou for any advice


    roger
     
  11. Oct 24, 2004 #10

    shmoe

    User Avatar
    Science Advisor
    Homework Helper

    if [tex]f(x)=3x^2 + 5x +9[/tex]

    f(junk) tells you to take your expression for f(x) and replace every x you see with "junk", whatever the junk is. Don't hold out on the brackets, they are inexpensive.

    [tex]f(x+3)=3(x+3)^2 + 5(x+3) +9[/tex]

    Expand out if you wish to simplify.

    f(ax) is the function applied to ax, so

    [tex]f(ax)=3(ax)^{2}+5(ax)+9=3a^{2}x^{2}+5ax+9[/tex]

    af(x) is the function applied to x, then the whole thing multiplied by a:

    [tex]af(x)=a(3x^{2} + 5x +9)=3ax^{2}+5ax+9a[/tex]


    Using f(x) as above can you find f(y)? f(x+2y)? f(x^2)? (f(x))^2?
     
  12. Oct 25, 2004 #11

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Nicely done, Shmoe
     
  13. Oct 25, 2004 #12
    Dear Shmoe,

    I've had a go, is this correct :

    f(y) = 3y^2 + 5y + 9

    f(x+2y) = 3(x+2y)^2 +5(x+2y) + 9

    f(x^2) = 3x^4 + 5x^2 + 9

    (f(x))^2 = (3x^2+5x+9)^2

    But what does it actually mean by f(y) ?
    Does it mean y is a function of x ?


    thanx


    roger
     
  14. Oct 25, 2004 #13

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    All your go's are correct.
    Without any other specification, inserting "y" in the x-place, (that is, in your first equation),
    you've simply changed the variable name from "x" to "y" (just a notational change).
     
  15. Oct 25, 2004 #14
    > f(x+2y) = 3(x+2y)^2 +5(x+2y) + 9

    In this example, you say that f depends on x and also on y, so it is a function of x and y and it is written as f(x,y). The trick of shmoe is valid, but don't forget that the information given between the brackets is the dependance of the function.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: F(x), G(x) Etc
  1. F(x) problem? (Replies: 5)

  2. F(x,v) = kvx (Replies: 5)

  3. Torque = r x F (Replies: 4)

Loading...