Composite functions

1. Aug 4, 2008

fr33pl4gu3

Can anyone help me solve this question??

Given f(x) = x2- 16 and g (x) = √x-3, find f(x) - g(x), g(x)/f(x), f(x)g(x) and (fog)(x) and state their domains.

Last edited: Aug 4, 2008
2. Aug 4, 2008

tiny-tim

Welcome to PF!

Hi fr33pl4gu3 ! Welcome to PF!

(have a square-root: √ and a squared: ² )

(do you mean √(x-3) or √(x) - 3? )

Show us what you've tried, and how far you've got, and then we'll know how to help you.

3. Aug 4, 2008

fr33pl4gu3

This is how i done it:

f(x) - g(x) = x2 - 16 - √x-3

g(x)/f(x) = √x-3 / x2 - 16

f(x)g(x) = (x2-16)(√x-3)

(fog)(x) = √x2-19

I wonder if this is correct.

Last edited: Aug 4, 2008
4. Aug 4, 2008

tiny-tim

Hi fr33pl4gu3!

Show us in detail how you got it.

5. Aug 4, 2008

fr33pl4gu3

The last one is it done in this way:

(fog)(x) = f(√x-3) = (√x-3)2 - 16 = x-19

6. Aug 4, 2008

HallsofIvy

Staff Emeritus
No, the first one is NOT correct. It is f(x)- g(x)= x2+ 16- (√(x)- 3) which is NOT x2+ 16- √(x)- 3.

(I am assuming that, by √(x)- 3, you mean √(x)- 3 and not √(x- 3). Tiny-tim is apparently assuming you meant √(x- 3). You never did answer tiny-tim's question.)

7. Aug 4, 2008

tiny-tim

Hi fr33pl4gu3!
Yes, that's right!

Are you ok with the domains?