Please write steps in detail for this question..I\'ve been havign a tough time with inverse functions and really need to understand the steps better. Thanks in advance! Solution f(x) = 3-2x y = 3-2x y-3 = -2x 2x = 3-y x = (3-y)/2 f^-1(y) = (3-y)/2 inverse of f(x) = f^-1(x) = (3-x)/2 g(x) = (x+1)/(x-3) y = (x+1)/(x-3) y*(x-3) = x+1 xy-3y = x+1 x(y-1) = 3y+1 x = (3y+1)/(y-1) g^-1(y) = (3y+1)/(y-1) inverse of g(x) = g^-1(x) = (3x+1)/(x-1) h(x) = 2x/(x-3) y = 2x/(x-3) y*(x-3) = 2x xy -3y = 2x x(y-2) = 3y x = 3y/(y-2) h^-1(y) = (3y)/(y-2) inverse of h(x) = h^-1(x) = (3x)/(x-2) .

1. Please write steps in detail for this question..I've been havign a tough time with inverse
functions and really need to understand the steps better. Thanks in advance!
Solution
f(x) = 3-2x
y = 3-2x
y-3 = -2x
2x = 3-y
x = (3-y)/2
f^-1(y) = (3-y)/2
inverse of f(x) = f^-1(x) = (3-x)/2
g(x) = (x+1)/(x-3)
y = (x+1)/(x-3)
y*(x-3) = x+1
xy-3y = x+1
x(y-1) = 3y+1
x = (3y+1)/(y-1)
g^-1(y) = (3y+1)/(y-1)
inverse of g(x) = g^-1(x) = (3x+1)/(x-1)
h(x) = 2x/(x-3)

2. y = 2x/(x-3)
y*(x-3) = 2x
xy -3y = 2x
x(y-2) = 3y
x = 3y/(y-2)
h^-1(y) = (3y)/(y-2)
inverse of h(x) = h^-1(x) = (3x)/(x-2)