Inverse Of A Function: find inverse of f(x) = -(3x - 1) / x

[khanderson22]

Just need a little help with the Algebra in finding the inverse function of -(3x-1)/x.

 

[Loren]

Re: Inverse Of A Function

y = -(3x-1)/x
\(\displaystyle y = \frac{-(3x-1)}{x}\)

To get the inversde function, interchange the x and y's and solve for y.
\(\displaystyle x = \frac{-(3y-1)}{y}\)

Now, solve for y.

 

[khanderson22]

Re: Inverse Of A Function

Yes I understand how to find the inverse of the function, just have gone blank and cant seem to do the algebra to get it there. Sorry for the confusion.

 

[mmm4444bot]

Did you try?

Hello KH:

You did not ask any question or show any work, so it is not possible for me to understand what you would like anybody to do for you.

Were you able to start anything at all?

I'm assuming that you did, since you state that you "just need a little help with the algebra"?

Please show us what you've done so far, and then tell us why you're stuck.

If you have not yet begun any algebra, then here's how to get started.

Write the function output for f(x) as y.

y = -(3x - 1)/x

Switch the input and output.

x = -(3y - 1)/y

Solve for y to find the inverse definition for f(x).

Cheers,

~ Mark

 

[mmm4444bot]

Re: Inverse Of A Function

... just have gone blank and cant seem to do the algebra to get it there.

You are trying to solve for a variable that appears in the denominator of a fraction. This is always a clue to multiply both sides by that variable because this is the only way to get it out of the denominator.

Collect all of the terms that contain the variable on one side of the equals sign.

Factor.

Solve.

Please post your work.

Thank you.

 

[khanderson22]

Re: Inverse Of A Function

Hi Mark,

So far I've tryed this:

1. Moving the y to the left-
yx=-3y-1
2. So should i-
yx+3y=1
3. Then
y(x+3)=1
4. Finally
y=1/(x+3)

Thank you very much for the help!

 

[mmm4444bot]

Re: Inverse Of A Function

... Finally y=1/(x+3)

Good job. Do you know how to check your result?

f(x) = b

f[sup:3k5j8enk]-1[/sup:3k5j8enk](b) = x

If you take the output of f(x) and use it as an input in f[sup:3k5j8enk]-1[/sup:3k5j8enk](x), then f[sup:3k5j8enk]-1[/sup:3k5j8enk](x) will output the same expression used as an input to f(x).

In other words, one function "undoes" the other.

If you input the expression 1/(x + 3) into f(x), then you should get x as an output.

If you input the expression (1 - 3x)/x into f[sup:3k5j8enk]-1[/sup:3k5j8enk](x), then you should get x as an output.

~ Mark