Posted by **anonymous** on Wednesday, January 9, 2013 at 6:01pm.

Consider the functions

f(x)=2x+8/x+6; g(x)=6x-8/2-x

Find f(g(x))

Find g(f(x))

Deterrmine if f and g are inverses of each other.

a. What is f(g(x))?

Give any values of x that need to be excluded from f(g(x))

x=?

b. what is g(f(x))?

ive any values of x that neeedd to be excluded from g(f(x))

x=?

c. Are the functions f & g inverses of each other ?

**Please show work**

- math-please I really need help!!!!! -
**Reiny**, Wednesday, January 9, 2013 at 6:28pm
Surely you mean

f(x) = (2x+8)/(x+6) and g(x) = (6x-8)/(2-x)

f(g(x)) = (2(6x-8)/(2-x) + 8)/((6x-8)/(2-x) + 6)

multiply by (2-x)/(2-x)

= (2(6x+8) + 8(2-x))/(6x-8 + 6(2-x))

= (12x-16 + 16 - 8x)/(6x-8 + 12 - 6x)

= 4x/4

= x

check:

let x=4

g(x) = 16/-2 = -8

then f(g(4))

= f(-8) = (-16+8)/(-8+6) = -8/-2 = 4

I will leave it up to you to find g(f(x))

but you should also get x as a final answer

If f(x) and g(x) are any functions so that

f(g(x)) = x, then the two functions are inverses of each other.

We have that situations, so they are inverses of each other

or .... the long way ... actually find the inverse of one of them

let y = (2x+8)/(x+6)

inverse is

x = (2y + 8)/(y+6)

xy + 6x = 2y + 8

xy - 2y = 8 - 6x

y(x-2) = (8-6x)

y = (8-6x)/(x-2) = (6x-8)/(2-x) which is the other function.

## Answer This Question

## Related Questions

- pre calculus - consider the functions f(x)=x^3-3 and g(x)=3 sqrt x+3: a. find f(...
- algebra - consider the functions f(x)=9/x; and g(x)=9/x what is f(g(x))? give ...
- College Algebra! help! - Consider the following functions f(x)= (7x+8)/(x+3) and...
- Consider the functions - Consider the functions f(x)= 5x+4/x+3(This is a ...
- Math Need Immediate Help???? - Find the inverses of each of the functions below ...
- math - The application of one function followed by the application of a second ...
- Precalculus - The application of one function followed by the application of a ...
- Algebra-Functions - Could you please check my answers and help me with two ...
- Math - Again, I'm learning about trigonometric functions. I need to find the ...
- math - consider the function f(x)=2x+8/x+6, g(x)=6x-8/2-x a. what is f(g(x))? b...

More Related Questions