If f(x) = 5x - 6, what is the equation for f^-1(x)?

CPhill is right.

THE INVERSE OF A FUNCTION IS THE EQUATION OF THE FUNCTION'S IMAGE WHEN IT IS REFLECTED ABOUT THE LINE Y=X     (This is important to know)

I just swap the letters around right from the beginning and then rearrange

y=5x+6 becomes

x=5y+6

$$y=\frac{x-6}{5}\\\\
f^{-1}(x)=\frac{x-6}{5}\\\\$$

If f(x) = 5x - 6, what is the equation for f^-1(x)

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So, we want to find the inverse of this......there are  couple of ways to do that......let's look at one

First.....let's write this as

y = 5x - 6      ..........now let's get "x" by itself......add 6 to both sides

y + 6 = 5x     ..........divide both sides by 5

(y + 6)/ 5  = x      ....now, just "switch" x and y

(x + 6)/ 5  = y      

If we have an inverse - and we do - it simply"reverses" the x and y coordinates - in "math" terms, if (a,b) is on the original graph, then (b,a) is on the inverse graph. Let's pick a point on the original graph, say, (6,24). So (24,6) should be on the on the inverse graph - and it is!! This is always a good way to check to see if the "inverse" is correct.

One more thing...... replace the "y" on the inverse with f^-1(x) 

So we have ..... f^-1(x) = (x + 6)/ 5

And that's it....