Question

Find the inverse function algebraically. Show all steps and proper notation.

f(x)=x+4/3

Please show all work
Thank you! :)))

Answer 1

Explanation:

First, are you sure that's the right equation, x + 4/3? I ask only because the fraction is a little odd.

So I found this on a university's website:

1. Replace f(x) by y in the equation describing the function.
2. Interchange x and y. In other words, replace every x by a y and vice versa.
3. Solve for y.
4. Replace y by
   `f^(-1)`(x).

The first step isn't much of a step, it just says to call "f(x)" y. Which it usually is anyway, right? Because you typically plug in a value for x, find the output of the function, and plot that as the y coordinate. So:

y = x + 4/3

Second step, interchange x and y:

x = y + 4/3

Third step, solve for y:

y = x - 4/3

Fourth step, now call y the inverse function of f(x):

`f^(-1)`(x) = x - 4/3

The webpage started out by saying that an "inverse function" simply undoes whatever was done to x, and here you can see that plainly: 4/3 was added to x before, so to undo that you have to subtract it.

They give an example that illustrates that a little better:

f(x) = 3x + 2

Now there are two things acting on x, the multiplier of 3, and adding 2. So those are the two things that will have to be undone. Using the steps above:

y = 3x + 2

x = 3y + 2

3y = x - 2

y = (x-2)/3

That's the inverse function, and you can see in it how the 3-times and the plus+2 were "undone."

Here's that website:

dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/functions/inverse/inverse.html