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f(x)=18x^2-3x
\n" ); document.write( "g(x)=20x-2
\n" ); document.write( "c=9
\n" ); document.write( "find fog(c).
\n" ); document.write( "fog(c) means f(g(c)).
\n" ); document.write( "this translates to f of (g of c).
\n" ); document.write( "first find g(c).
\n" ); document.write( "you know that g(x) = 20x-2.
\n" ); document.write( "if you replace x with c, then you get:
\n" ); document.write( "g(c) = 20c-2.
\n" ); document.write( "you have just found g(c).
\n" ); document.write( "now you want to find f(g(c)).
\n" ); document.write( "start with f(x) = 18x^2 - 3x.
\n" ); document.write( "you need to replace x with g(c).
\n" ); document.write( "f(x) = 18x^2 - 3x becomes:
\n" ); document.write( "f(g(c)) = 18*g(c)^2 - 3*g(c)
\n" ); document.write( "since you know that g(c) is equal to 20c-2, then you can replace g(c) with 20c-2 to get:
\n" ); document.write( "fog(c) = f(20c-2) = 18*(20c-2)^2 - 3*(20c-2)
\n" ); document.write( "x was the argument of the f(x) = 18x^2 - 3x
\n" ); document.write( "x was replaced with the new argument of g(c) which was then replaced with the new argument of (20c-2) because g(c) = 20c-2.
\n" ); document.write( "you now have:
\n" ); document.write( "fog(c) = f(20c-2) = 18(20c-2)^2 - 3(20c-2)
\n" ); document.write( "since you know that c = 9, you can replace c with 9 in the expression to get:
\n" ); document.write( "fog(c) = f(g(c)) = 18*(20c-2)^2 - 3*(20c-2) becomes:
\n" ); document.write( "fog(9) = f(g(9)) = 18*(20*9-2)^2 - 3*(20*9-2) which becomes:
\n" ); document.write( "fog(9) = f(g(9)) = 18(178)^2 - 3(178) which becomes:
\n" ); document.write( "fog(9) = f(g(9)) = 569778\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "in any function, the argument of the function is what is enclosed in parentheses.
\n" ); document.write( "normally, the independent variable is the argument.
\n" ); document.write( "that's why you see f(x) = 18x^2 - 3x
\n" ); document.write( "x is the independent variable.
\n" ); document.write( "it is also the argument to the function.
\n" ); document.write( "the function itself is a set of rules that relates the independent variable to the dependent variable.
\n" ); document.write( "this equation used to be called y = 18x^2 - 3x
\n" ); document.write( "x was the independent variable.
\n" ); document.write( "y was the dependent variable.
\n" ); document.write( "that hasn't really changed.
\n" ); document.write( "all that's changed is we now call the dependent variable the function and we show what the argument to the function is.
\n" ); document.write( "so y was replaced with f(x).
\n" ); document.write( "we could also have called it y(x). the name doesn't matter for anything other than to identify the particular set of rules expressed by that particular equation.
\n" ); document.write( "the argument to the function is what you feed the equation in order to get the value of the function.
\n" ); document.write( "f(x) = 18x^2 - 3x is the function.
\n" ); document.write( "the argument x is fed to the equation.
\n" ); document.write( "the equation evaluates x by the set of rules of the equation.
\n" ); document.write( "f is the name of this particular function to distinguish it from other functions, like g(x) or t(x) or abc(x) or nbc(x).
\n" ); document.write( "those are just names of functions to distinguish them from other functions.
\n" ); document.write( "f(x) = 18x^2 - 3x can be translated to:
\n" ); document.write( "f(argument) = 18*argument^2 - 3*argument.
\n" ); document.write( "whatever the argument is determines what the function named f is working on.
\n" ); document.write( "the function named f does the same thing to any argument presented to it.
\n" ); document.write( "it first squares the argument and then multiplies it by 18 and than adds 3 times the argument to get a total result which then represents the value of the function.
\n" ); document.write( "that's why f(x) = 18x^2 - 3x becomes f(g(c)) = 18*(g(c))^2 - 3*(g(c)) which then becomes f(20c-2) = 18*(20c-2)^2 - 3*(20c-2) which then becomes f(9) = 18*(20*9-2)^2 - 3*(20*9-2).
\n" ); document.write( "it's the same equation being applied to the new argument each time.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the very simple way to solve this problem would have been to do the following:
\n" ); document.write( "problem:
\n" ); document.write( "f(x)=18x^2-3x
\n" ); document.write( "g(x)=20x-2
\n" ); document.write( "c=9
\n" ); document.write( "find fog(c).
\n" ); document.write( "solution:
\n" ); document.write( "g(x) = 20x-2
\n" ); document.write( "g(c) = 20c-2
\n" ); document.write( "g(9) = 20*9-2 = 178
\n" ); document.write( "g(c) = 178 when c = 9
\n" ); document.write( "f(x) = 18x^2 - 3x
\n" ); document.write( "fog(c) = f(g(c)) = f(178)
\n" ); document.write( "f(178) = 18*178^2 - 3*178 = 569778\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "before you can do that, you have to know and understand how the process works.
\n" ); document.write( "hopefully this answer will have helped you to do so.\r
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