Respuesta :
It’s actually F(G(x))=x . I plugged in the other answer and got it wrong.
The correct answer is:
B) f(g(x)) = x.
Explanation:
A composition of two inverse functions undoes everything except the variable used.
Using x, g(x) will perform some action to x. f(x), since it is the inverse of g(x), will undo the action that g(x) performed; this will simply leave x.
For example, let f(x) = x-3. To find the the inverse, g(x), we will first replace f(x)= with y=:
y = x-3
Now we switch x and y:
x = y-3
To isolate y, we add 3 to each side:
x+3 = y-3+3
x+3 = y
Now we write this as g(x):
g(x) = x+3
We now perform the composition f(g(x)):
g(x) = x+3
f(g(x)) = f(x+3) = x+3-3 = x
B) f(g(x)) = x.
Explanation:
A composition of two inverse functions undoes everything except the variable used.
Using x, g(x) will perform some action to x. f(x), since it is the inverse of g(x), will undo the action that g(x) performed; this will simply leave x.
For example, let f(x) = x-3. To find the the inverse, g(x), we will first replace f(x)= with y=:
y = x-3
Now we switch x and y:
x = y-3
To isolate y, we add 3 to each side:
x+3 = y-3+3
x+3 = y
Now we write this as g(x):
g(x) = x+3
We now perform the composition f(g(x)):
g(x) = x+3
f(g(x)) = f(x+3) = x+3-3 = x
