Question

Find the inverse of each of these functions
a)f(x)=x/x+2
b)f(x)=2x/5-x
c)f(x)=3x/2x+1

Answer 1

x =2y/5 -y
5x = 2y -5y
5x = -3y
F(x) = -5x/3

Answer 2

1st one:

if f(x) = x/(x+2) , then y = x/(x+2)

step1: interchange the x and y variables to get the inverse as

x = y/(y+2)

step 2: solve this new equation for y

x = y/(y+2)
xy + 2x = y
xy - y = -2x
y(x-1) = -2x
y = -2x/(x-1) or y = 2x/(1-x)

f^-1 (x) = 2x/(1-x)

now do the same for others following these two steps.