Composite Functions: f o g (x) = Abs(x), f(x) = root(x), g(x) = Abs(x)

[Larrytsai]

f o g (x) = Abs(x)
f(x)=?
g(x)= root(x)

im thinking f(x) is = to root(x) correct me if I am wrong?

 

[Mark44]

f(x) = sqrt(x) doesn't work. Are you sure you have this problem written correctly? Could it be g o f (x) = Abs(x)? That would make more sense with g(x) being sqrt(x). Of if it is indeed f o g (x) = Abs(x), could it be that f(x) = sqrt(x) and you need to find g(x)?

 

[Larrytsai]

its correct way i took it straight from the book.

 

[Mark44]

OK.
If f(x) = x² and g(x) = $$\sqrt{x}$$
then $(f~\circ~g )(x) = x$.

Since the domain of g = {x | x $\geq$ 0}, then x = |x| in this case.