Composite functions f(g(h(x)))

[flakine]

Find f o g o h, where

f(x)= √(1-x)
g(x) 1-x^2
h(x)=1+√x

This is where I am:

g(h(x)) 1-(1+√x)^2
1-(1+2√x+x)
1-1-2√x-x
g(x)=-2√x-x
f(g(x))=√(1+(-2√(x)-x)

What am I doing wrong?

 

[askmemath]

You've copied the signs wrong!!

f(x) = sqrt(1-x)

= sqrt( 1 - (-2sqrtX - X))

= sqrt( 1 + 2sqrtX + X)

= sqrt((1+ X)^2)

= 1+X

ta daaaa!!!

 

[flakine]

Are you sure that's it? The book has:

1+√(x)

 

[askmemath]

OOps my mistake it should read as

sqrt((1+sqrt(x))^2)

= 1 + sqrtX

ta daaaaa!!!![/b]

 

[flakine]

Thanks!

 

[mathmike]

Find f o g o h, where

f(x)= √(1-x)
g(x) 1-x^2
h(x)=1+√x

It is simlier other way around:
f(g) = sqrt(1-(1-x^2)) = x, x>=0
f(g(h)) = 1 + sqrt(x)