SOLUTION: If (x)=8-3x, then find f^-1 (14). Is it -34, -2, 2, -1/34? please help. thank-you.

Algebra ->  Graphs -> SOLUTION: If (x)=8-3x, then find f^-1 (14). Is it -34, -2, 2, -1/34? please help. thank-you.      Log On


   

Question 202896: If (x)=8-3x, then find f^-1 (14). Is it -34, -2, 2, -1/34? please help. thank-you.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The notation f%5E%28-1%29%28x%29 stands for "the inverse of f(x)". The inverse of f(x) is the relation you get when you swap the x and y in the equation for f(x). (Note: The Algebra.com's software incorrectly puts a multiplication symbol in the middle of f%5E%28-1%29%28x%29. Please ignore it.)

We'll start by figuring out f%5E%28-1%29%28x%29 and then use it to find f%5E%28-1%29%2814%29.

To find the inverse of f(x):
  1. Rewrite it with a "y" in the place of f(x):
    y+=+8+-+3x
  2. Rewrite the equation with x's where the y's are and y's are the x's are:
    x+=+8+-3y
    This is the inverse equation.
  3. Solve the inverse equation for y:
    Subtract 8 from both sides:
    x+-+8+=+-3y
    Divide both sides by -3:
    %28x+-+8%29%2F%28-3%29+=+y
  4. Replace the "y" with f%5E%28-1%29%28x%29:
    %28x+-+8%29%2F%28-3%29+=+f%5E%28-1%29%28x%29

Now we will find f%5E%28-1%29%2814%29:
f%5E%28-1%29%2814%29+=+%28%2814%29+-+8%29%2F%28-3%29
Simplifying we get
f%5E%28-1%29%2814%29+=+6%2F%28-3%29
f%5E%28-1%29%2814%29+=+-2