How do I find the inverse function of this one:
f(x)=(3x-1)/(x+5)

Question

How do I find the inverse function of this one:
f(x)=(3x-1)/(x+5)

e.mccormick · Answer

Same as any invese.  Put in y for x and x for f(x), then solve for y.

e.mccormick · Answer

$f(x)=\dfrac{3x-1}{x+5}  $ becomes

$x=\dfrac{3y-1}{y+5}  $  Now solve for y.

hero · Answer

@danielle02, do you know how to finish solving for y?

anonymous · Answer

@Hero no, I don't.

yttrium · Answer

Do you know cross multiplication? If you, you can apply it.

yttrium · Answer

That is actually like this.
x(y+5) = 3y - 1
expand the left term and after that, isolate all terms having y to the left and all terms not having y to the right.
Then, factor out y to the left and then there it is by equating the equation by y.

hero · Answer

To finish solving for y, do this:

Multiply both sides by (y + 5):
$$x(y + 5) = 3y + 1$$

Distribute $x$ to $y + 5$:
$$xy + 5x = 3y + 1$$

Subtract 3y from both sides; Add 5x to both sides:
$$xy - 3y = 1 - 5x$$

Factor $y$ from $xy - 3y$:

$$y(x - 3) = 1 - 5x$$

Divide both sides by (x - 3)
$$y = \frac{1- 5x}{x -3}$$

The last step is to replace $y$ with $f^{-1}(x)$
$$f^{-1}(x) = \frac{1- 5x}{x -3}$$

anonymous · Answer

Ok, I understand now. Thanks for the help.