Does anyone kno what fog and gof means....?

Question

I've got this question that
i can figure out but i can't find out
anywhere in my text book where fog and gof are
and i can't finish the equation.

Thanks for any help

Answer 1

fog means f [g(x)]

gof means g [f(x)]

(just a "misprint" or "typo" in the Maths B assignment

Answer 2

fog means f as a function of g

say you have two functions

f(x)= x-1 and g(x) = 4x

fog =(4x)-1

you just substitute the g in for the x of f(x)

and vice versa for gof

Answer 3

fog and gof are shorthand for the function you're doing.
If f(x) = 2x
and g(x) = x - 3

then fog = 2(x-3)
and gof = (2x) - 3
in other words, replacing the x in f(x) with g(x), and vice versa.

Answer 4

Rather than enter into a long winded explanation let us consider a few examples:-
Example 1
Let f(x) = 3x and g(x) = x² then:-
(fog)(x) = f(g(x)) = f(x²) = 3x²
(gof)(x) = g(f(x)) = g(3x) = 9x²
Example 2
Let f(x)= 4x and g(x) = sin x
(fog)(x) = f(g(x)) = f(sinx) = 4 sinx
(gof)(x) = g(f(x)) = g (4x) = sin 4x

Hope these examples are of use.

Answer 5

That notation is sometimes used in place of

f(g(x)) and g(f(x)). It is called "composition of functions"

They use the little o to distinguish it from a multiplication dot because it's not multiplication.

Answer 6

I assume you mean something like f°g, g°f (with the circle in the middle of the line).
f°g simply means f(g).
Example:

f(x) = x²
g(x) = x+1
f°g (x) = f(g(x))= f(x+1) = (x+1)²
g°f(x) = g(f(x)) = g(x²) = x² +1
(in this case f°g (x) =|= g°f(x)).