Inverse Functions

Question

How do I find the inverse function of f(x)=-(4/x+2)-3

Answer 1

Watch the parenthesis!!!

 

Y=-(4/X+2)-3

   = -4/x-2-3

  = -4/x-5

 

Swapping x and y:

X= -4/y-5

 

Solving for y:

X+5=-4/y

 

Y= -4/(x+5)

 

Answer 2

f(x) = -4/(x+2) - 3

 

1.  replace f(x) with y

y= -4/(x+2) - 3

 

2.  swap x and y in the equation

x = -4/(y+2) - 3

 

3. Solve for y

x + 3 = -4/(y+2)

(y+2)(x+3) = -4

xy + 3y + 2x + 6 = -4

y(x+3) = -2x - 10

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

 

4. Replace y with f^-1(x)

 

f^-1(x) = -2(x+5)/(x+3)