Amy's Reflection #4

How to Find the Inverse of a Function:

• Replace f(x) with y
• Reverse the roles of x and y
• Solve for y in terms of x
• Replace y with f-1(x)

Example 1 - f(x) = 2x + 3

1. write the function as an equation: y = 2x + 3
   
2. solve for x: x = (y - 3)/2
   
3. now write f-1(y) as follows .
   f -1(y) = (y - 3)/2 or f -1(x) = (x - 3)/2
   
4. Check:
   

• f(f -1(x))=2(f -1(x)) + 3
  =2((x-3)/2)+3 =(x-3)+3 =x
  
• f -1(f(x))=f -1(2x+3)
  =((2x+3)-3)/2 =2x/2 =x

Eample 2 - f(x) = √x + 4

1. (x)^2 = (√y + 4)^2
2. x^2 = y + 4
3. y = x^2 - 4
4. f-1(x) = (x^2 - 4)

• f(f-1(x)) = f(x^2 - 4) = √(x^2 - 4) + 4 = x
• f-1(f(x)) = f-1(√x + 4) = (√x + 4)^2 - 4 = x + 4 - 4 = x

ok im kinda nervous about tomorrow's test; i understand most of it but im afraid that im gonna freak out and forget...hopefully not. ok..umm..one question: we only have to the range for polynomails & absolute values, right?