Expert: Bobby Soltani - 4/9/2005

Question
f(x)= 1-3x is one-to-one
find the formula for f-1(inverse)
what is the domain of f-1
 what is the range of f
 what is the range of f-1

Answer
Hi Donald,

To find the inverse, you simply interchange the x and y, and then solve for y.  Here's how:

y = 1 - 3x
interchange x and y
x = 1 - 3y
subtract 1 from both sides
-3y = x - 1
divide both sides by -3
y = (-1/3)x + 1/3
so,
f^-1(x) = (-1/3)x + 1/3

Both functions are lines that have domains of all x's and ranges of all y's.

Notice that the inverse of a function will be a reflection of the function about the line y = x.

Let me know if you have any questions.

Bobby