# math-please I really need help!!!!!

posted by .

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 ?

• math-please I really need help!!!!! -

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.

## Similar Questions

1. ### Algebra-Functions

Could you please check my answers and help me with two problems?
2. ### Math

Again, I'm learning about trigonometric functions. I need to find the missing information for each triangle. I have the length of one leg as 24 and the opposite theta as 72. I need to figure out the other angles and side lengths, but …
3. ### algebra

consider the functions f(x)=9/x; and g(x)=9/x what is f(g(x))?
4. ### Precalculus

The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the …
5. ### math

The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the …
6. ### pre calculus

consider the functions f(x)=x^3-3 and g(x)=3 sqrt x+3: a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverses of each other. I really need help with these, I don't get it at all.
7. ### Consider the functions

Consider the functions f(x)= 5x+4/x+3(This is a fraction) and g(x)= 3x-4/5-x(This is a fraction) a)Find f(g(x)) b)Find g(f(x)) c)Determine whether the functions f and g are inverses of each other.
8. ### College Algebra! help!

Consider the following functions f(x)= (7x+8)/(x+3) and g(x)= (3x-8)/(7-x) (a) Find g(g(x)) (b) Find g(f(x)) (c) Determine whether the functions f and g are inverses of each other.
9. ### Math Need Immediate Help????

Find the inverses of each of the functions below algebraically. a.f(x)=3y+5x=18 b.h(t)=−4.9(t+3)^2+45.8
10. ### math

consider the functions f(x)=2x-8 and g(x)=x/2+4 (a) Find f(g(x)). (b) Find g(f(x)). (c) Determine whether the functions f and g are inverses of each other (a) What is f(g(x))?

More Similar Questions