SOLUTION: Please help me find the inverse of the function f(x)= log base 4 16x

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Question 268086: Please help me find the inverse of the function f(x)= log base 4 16x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+log%284%2C+%2816x%29%29

To find the inverse of a function:
  1. Replace the function notation with "y".
  2. Swap the x's and y's. After this you have the equation for the inverse.
  3. Solve the inverse equation for y, if possible.

Let's see how this works with your function.
1) Replace the function notation
y+=+log%284%2C+%2816x%29%29
2) Swap the x's and y's
x+=+log%284%2C+%2816y%29%29
3) Solve for y. We start by rewriting the equation in exponential form:
4%5Ex+=+16y
Next, divide both sides by 16:
4%5Ex%2F16+=+y
Since we were able to solve for y, the inverse of your function is itself also a function. This equation may be an acceptable answer. Or you may want to write this with function notation for an inverse:
4%5Ex%2F16+=+f%5E%28-1%29%28x%29
(Note: Algebra.com's formula software does not handle inverse notation well. It shows a multiplication symbol which does not belong.)

Also, since 16 is a power of 4, we can simplify the left side:
4%5Ex%2F4%5E2+=+f%5E%28-1%29%28x%29
4%5E%28x-2%29+=+f%5E%28-1%29%28x%29