Posted by **Rosie** on Tuesday, May 14, 2013 at 10:32pm.

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.

- College Algebra! help! -
**Reiny**, Tuesday, May 14, 2013 at 10:47pm
a)

g(g(x))

= g((3x-8)/(7-x)

= [3(3x-8)/(7-x) - 8]/( 7 - (3x-8)/(7-x) )

= [ (9x-24-56+8x)/(7-x)] / (49-7x-3x+8)/(7-x)]

= (17x - 80)/(57 - 10x)

b) do this in the same way I just showed you

c) let's take the inverse of f(x)

let y = (7x+8)/(x+3)

for the inverse, interchange the x and y

x = (7y+8)/(y+3)

xy + 3x = 7y + 8

xy - 7y = 8-3x

y(x-7) = 8-3x

y = (8-3x)/(x-7) = (3x - 8)/(7 - x) = g(x)

yes , they are inverses of each other.

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