# Thread: Inverse function

1. ## Inverse function

Find the inverse function for f (x) = 5x over x + 3 in the form of y = f to the power of - 1 (x)

How would I work this out anyone?

2. ## Re: Inverse function

Originally Posted by mathsgirl123431
Find the inverse function for f (x) = 5x over x + 3 in the form of y = f to the power of - 1 (x)
How would I work this out anyone?
Solve for $\displaystyle y$ in $\displaystyle x=\frac{5y}{y+3}$.
Then $\displaystyle f^{-1}(x)=y$

3. ## Re: Inverse function

is that the answer or is there more to do after that? i've never done these before! thanks for replying

4. ## Re: Inverse function

Originally Posted by mathsgirl123431
is that the answer or is there more to do after that? i've never done these before! thanks for replying
NO You solve $\displaystyle x=\frac{5y}{y+3}$ for $\displaystyle y$. When you do that you get $\displaystyle y=g(x)$, function of $\displaystyle x$.

Then set $\displaystyle f^{-1}(x)=g(x)$

5. ## Re: Inverse function

Originally Posted by mathsgirl123431
is that the answer or is there more to do after that? i've never done these before! thanks for replying
Plato told you what to do. You still have to do it yourself! (Do you know the definition of "inverse function". You might want to compare that to what Plato told you.

6. ## Re: Inverse function

Sorry guys, okay well this is what I tried myself:

y = 5x/(x + 3)

Next, switch the x and y variables, and re-write the function as:

x = 5y/(y + 3)

Now, solve this equation for y:

x(y + 3) = 5y

xy + 3x = 5y

3x = 5y - xy

3x = y(5 - x)

y = 3x / (5 - x)

Solution: f^-1(x) = 3x / (5 - x)

Thanks for the advice, I did work it out right didn't I?