The function f(x)=2x+2 is one-to-one. Find an equation for f^-1(x), the inverse function

Question

Type an expression for the inverse. Use integers or fractions for any numbers in the expression 

Answer 1

f(x) = 2x + 2

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

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

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

Answer 2

y = 2x + 2

 

X and Y switch places:

x = 2y + 2 

 

 

Now solves for y:

 

x - 2 = 2y

 

y = (x-2)/2

 

Check: f composition f-inverse

    2( x-2)/2 + 2 =  x- 2 + 2 = x

 

Check: f-inverse composition f:

   (2x + 2 - 2)/2 = 2x/2 = x

 

So the inverse is  y = (x-2)/2