Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = the quantity x minus seven divided by the quantity x plus three. and g(x) = quantity negative three x minus seven divided by quantity x minus one.

f(x) = (x - 7)/(x + 3)
g(x) = (-3x - 7)/(x - 1)

Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. 

f(x) = the quantity x minus seven divided by the quantity x plus three. and g(x) = quantity negative three x minus seven divided by quantity x minus one.

f(x) = (x - 7)/(x + 3)
g(x) = (-3x - 7)/(x - 1)

anonymous · Answer

@ganeshie8 Can you help?

anonymous · Answer

@phi

phi · Answer

this requires a lot of algebra
simplify 
(g(x) - 7)/(g(x) + 3)

replace g(x) with its definition  = (-3x - 7)/(x - 1)

anonymous · Answer

Oh okay so (-3x - 7)/(x - 1) -7  / (-3x - 7)/(x - 1) +3?

phi · Answer

yes.  I would tackle the bottom first.  
$$ \frac{(-3x - 7)}{x-1} + 3 $$
use a common denominator of (x-1)  and combine the fraction and 3.
can you do that ?

anonymous · Answer

Yup thanks I just needed help starting :)