Finding the Inverse of f(x) = x/(x+4)

So the inverse is f^-1(x) = -4x \div (x-1).In summary, the conversation was about finding the inverse of the function f(x) = x \div (x+4). The method involved replacing f(x) with y and solving for x. However, the individual was having trouble reducing the amount of x to one. The correct solution is f^-1(x) = -4x \div (x-1).
  • #1
RidiculousName
28
0
Hello, I am trying to find the inverse of f(x) = x \(\displaystyle \div\) (x+4)

IIRC i need to replace f(x) with y and solve for x.

I've tried to do y = x \(\displaystyle \div\) (x+4) becomes y(x+4) = x then xy + 4y = x but I can't reduce the amount of x to one.

What am I doing wrong in this problem?
 
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  • #2
RidiculousName said:
Hello, I am trying to find the inverse of f(x) = x \(\displaystyle \div\) (x+4)

IIRC i need to replace f(x) with y and solve for x.

I've tried to do y = x \(\displaystyle \div\) (x+4) becomes y(x+4) = x then xy + 4y = x but I can't reduce the amount of x to one.

What am I doing wrong in this problem?

Hi Mr. Ridiculous, welcome to MHB! ;)

We can take it a couple of steps further:

xy + 4y = x
xy - x + 4y = 0
xy - x = -4y
x(y - 1) = -4y
x = -4y \(\displaystyle \div\) (y-1)
 
  • #3
Thanks! I forgot I could leave the right side of the equation as zero.
 

FAQ: Finding the Inverse of f(x) = x/(x+4)

What is an inverse function?

An inverse function is a mathematical relationship between two variables that "undoes" the effect of the original function. In other words, if the original function takes an input x and produces an output y, the inverse function takes the output y and produces the input x.

How do you find the inverse of a function?

To find the inverse of a function, you can use the following steps:1. Write the original function as y = f(x)2. Switch the x and y variables, so the new function is x = f(y)3. Solve for y in terms of x4. Replace y with f-1(x) to get the inverse function

When does an inverse function exist?

An inverse function exists when the original function is one-to-one, meaning that each input has a unique output. This can be determined by graphing the function and checking if it passes the horizontal line test. If a horizontal line intersects the graph at more than one point, the function is not one-to-one and an inverse function does not exist.

What is the notation for an inverse function?

The notation for an inverse function is f-1(x). This does not mean the reciprocal of f(x), but rather the inverse function of f(x). It is important to note that this notation does not indicate an exponent, but rather a different function.

How can inverse functions be used in real life?

Inverse functions have many real-life applications, such as in finance, physics, and engineering. They can be used to model relationships between variables, such as the relationship between distance and time in physics. Inverse functions also play a crucial role in cryptography, where they are used to encrypt and decrypt messages.

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