HELP me this is some hard stuff?

Question

F(x)=x2-2x-1 and g(x)=1-x find (fog)(x)

Answer 1

THis is called a composite function. Look at the function
F(x) = x^2 -2x -1

(fog)(x) means that everywhere you see an x in the function f(x), you should replace it with (1-x).

So, (fog)(x) = (1 - x)^2 - 2(1 - x) - 1

You can simplify this by expanding and collecting like terms

(fog)(x) = 1 - 2x + x^2 - 2 + 2x - 1
= x^2 - 2

Answer 2

well,

if I remember, (fog) is just f(x) evaluated at g(x)

so

f(x)=x^2-2x-1

then fog(x)=(1-x)^2-2(1-x)-1

then its just regular algebra

fog(x)=1-2x+x^2-2+2x-1
=x^2-2

I guess thats the right way to express the answer

better check what I have done here carefully
I may not have understood the question and I may have made an error

Answer 3

(fog)(x) = f(g(x))= f(1-x)= (1-x)^2-2(1-x)-1= 1-2x+x^2-2+2x-1= x^2-2

Answer 4

Are you sure you typed that right? Because what f(x) really means is F at point x. so usually they'll give you the formula and than say find f(2) so you'll but in 2 for all the x and get the answer. But right now I think that you should answer not even information.