SOLUTION: Find a formula for the inverse of the function. f(x) = 6x − 1/2x + 9 f −1(x) = (f inverse of x).

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Question 1196464: Find a formula for the inverse of the function.
f(x) = 6x − 1/2x + 9
f −1(x) = (f inverse of x).

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39613) (Show Source):
You can put this solution on YOUR website!
BAD NOTATION

You want , in pure text, f(x)=(6x-1)/(2x+9), and want to find f^(-1)(x).
Yet, your given function the way you showed is ambiguous.

Written to show better mathematical express,
, and you want to find .

Choosing I to represent the inverse of f just for easier symbolisation, then for finding I, you can make
, and solve this for I.

, but you may need to check for any restrictions.

Answer by greenestamps(13195) (Show Source):
You can put this solution on YOUR website!

If you are working on a problem like this, your knowledge of math should be enough for you to know that the proper use of parentheses is important. The function as you show it is this:

f(x) = 6x − 1/2x + 9 -->

That is almost certainly not what you intended; you probably meant

f(x) = (6x - 1)/(2x + 9) -->

Finding the inverse of a function like this is a common type of problem on high school math competition tests; there is an easy pattern that makes it easy to write down the inverse function without doing any work.

Let's take a generic example and find the inverse by the standard method of switching x and y and solving for the new y.

Now compare the original function to its inverse function:

-->

In the inverse, the B and C stay where they are, while the A and D switch places and both change sign.

Using this pattern, you can write down the inverse of your given function with little effort:

-->