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