Question

If f(x) = 2x + 10, then f-'(x) =

Answer 1

We need to find the inverse of the function:

`f(x)=2x+10`

First step:

replace f(x) with a letter (y for example):

`=2x+10`

y = 2x +10 (the equation editor is not allowing me to enter a "y" for some reason)

Second step:

solve for x:

2x = y - 10

x = (y - 10)/2

Third step:

replace x with f^-1(x), and replace y with x:

`f^(-1)(x)=(x-10)/(2)=(x)/(2)-5`

the inverse is: (1/2) x - 5

or equivalently: (x-10)/ 2 that is: (x minus 10) divided by 2