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

Algebra.Com
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(39617)   (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(13200)   (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:

-->


RELATED QUESTIONS

Find a formula for the inverse function f^-1 of the indicated function f. f(x)= 5 +... (answered by drk)
Find the inverse of the function.... (answered by nerdybill)
Find a formula for the inverse. f(x)=6x f^-1(x)= thank... (answered by josgarithmetic)
find the inverse function of 9+7x/5-6x... (answered by josgarithmetic)
Find the inverse function of f... (answered by ankor@dixie-net.com)
Find the inverse of the function (a) f(x)= x^2+2x-1,... (answered by josgarithmetic,MathLover1,Edwin McCravy)
find a formula for the inverse of the function if it exists f(x)=x/x-1 Thank you... (answered by stanbon)
Find the inverse function of f. 1. f(x)=1+3x/5-2x (answered by stanbon)
Given the function f(x)=2-1/7x Find a formula for the inverse... (answered by josgarithmetic)