Inverse Function of f(x)= x+3/x-4

[dishelton]

I have a problem where I am to find the inverse of
f(x)= x+3/x-4
I know that you write y=x+3/x-4
then you reverse x and y
x=y-4/y+3 and I am lost if you reverse the fraction.

 

[stapel]

...find the inverse of f(x)= x+3/x-4

As posted, the function is:

. . . . .\(\displaystyle f(x)\, =\, x\, +\, \frac{3}{x}\, -\, 4\)

Is that what you mean the function to be? Or is it one of the following?

. . . . .\(\displaystyle f(x)\, =\, x\, +\, \frac{3}{x\, -\, 4}\)

. . . . .\(\displaystyle f(x)\, =\, \frac{x\, +\, 3}{x}\, -\, 4\)

. . . . .\(\displaystyle f(x)\, =\, \frac{x\, +\, 3}{x\, -\, 4}\)

I know that you write y=x+3/x-4
then you reverse x and y
x=y-4/y+3 and I am lost if you reverse the fraction.

A good next step is to multiply through on both sides by the denominator. Then get all the "y" terms together on one side of the "equals" sign, factor out the "y", and divide through by whatever is multiplied on the "y". The result is the inverse.

Eliz.

 

[dishelton]

it is a fraction where x-4 is under x+3. Hope this is what you were wanting.

 

[Loren]

Dishelton. Your original post of "f(x)= x+3/x-4" should be posted as "f(x)= (x+3)/(x-4)". You then rewrite it as "y=(x+3)/(x-4)". Next, you interchange the x's and y's. "x= (y+3)/(y-4)". Now, solve for y. That will be the inverse function you are looking for.

 

[stapel]

it is a fraction where x-4 is under x+3.

Then switch the variables, and start solving the rational equation for "y=" by multiplying through by the new denominator, y + 3. You should end up with:

. . . . .xy + 3x = y - 4

Then solve the literal equation: Group the "y" terms together on one side of the "equals" sign, with all the other terms on the other side. Factor out the "y", and divide off whatever is left. The result will be the inverse.

If you get stuck, please reply showing how far you have gotten in following the steps. Thank you!

Eliz.