Friday

March 6, 2015

March 6, 2015

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

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 6:28pmSurely 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(...

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 ...

Algebra-Functions - Could you please check my answers and help me with two ...

Math - Inverse Functions - Find the inverses of the following functions. y = 3(x...

math - consider the functions f(x)=x^3-2 and g(x)=3 sqrt x+2: a. find f(g(x)) b...

math- precalculus - Help please! I can't seem to get x as the answer to prove ...

Math Homework - Hi! I really need help with these. I tried them on my own but I ...

algebra - consider the functions f(x)=9/x; and g(x)=9/x what is f(g(x))? give ...

math - 1. The following functions are inverses of each other: f(x) = 3x - 7 and ...