Solve Composite Functions: f(x), g(x), Domains | MathHelp

[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.

 

[tiny-tim]

Welcome to PF!

Can anyone help me solve this question??

Given f(x) = x^2 - 16 and g (x) = sqrtx-3, find f(x) - g(x), g(x)/f(x), f(x)g(x) and (fog)(x) and state their domains.

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.

 

[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.

 

[tiny-tim]

(fog)(x) = √x²-19

I wonder if this is correct.

Hi fr33pl4gu3!

Your first three are fine.

Your fog(x) isn't.

Show us in detail how you got it.

(and be more careful about where you put your brackets )

 

[fr33pl4gu3]

The last one is it done in this way:

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

 

[HallsofIvy]

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.)

 

[tiny-tim]

Hi fr33pl4gu3!

The last one is it done in this way:

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

Yes, that's right!

Are you ok with the domains?