Question

Find f o g and g o f to determine if f and g are inverse functions. If they are not inverses, pick the function that would be the inverse with f(x). f(x) = (-2/x) – 1; g(x) = -2/(x+1) Choices: a. g(x) has to be: (1+x)/2 b. g(x) has to be: x/2 c. g(x) has to be: 2 – (1/x) d. Inverses

Answer 1

(f o g) = x, then, g(x) is the inverse of f(x).

Explanation:

You have the following functions:

`f(x)=-(2)/(x)-1\\\\g(x)=-(2)/(x+1)`

In order to know if f and g are inverse functions you calculate (f o g) and (g o f):

`f\ o\ g=f(g(x))=-(2)/(-(2)/(x+1))-1=x+1-1=x`

`g\ o\ f=g(f(x))=-(2)/(-(2)/(x)+1)=-(2)/((-2+x)/(x))=(2x)/(2-x)`

(f o g) = x, then, g(x) is the inverse of f(x).