Sanity Checks are missives on a specific math point in need of clarification.
Somewhere back in the black mist, you probably learned that the way to get the graph of the inverse of a function is to reflect the graph of the function about the line y = x (you can also invert a function by algebra bargle, but that's not what we're after here).
But there's another way. It's obvious if you've seen it, but like many things the world seems divided into two camps: those who have seen the trick and those who haven't.
Here's the trick. Assume you have a piece of paper upon which is drawn the graph of the function of interest. To see what the graph of the inverse looks like:
1) Rotate the paper 90 degrees counter-clockwise.
2) Flip the paper over.
3) Hold the page up to a light so you can see through it.
Viola! You are now looking at the graph of the inverse of the function.
Want a handy diagram of the process? On a mug? Of course you do.
Somewhere back in the black mist, you probably learned that the way to get the graph of the inverse of a function is to reflect the graph of the function about the line y = x (you can also invert a function by algebra bargle, but that's not what we're after here).
But there's another way. It's obvious if you've seen it, but like many things the world seems divided into two camps: those who have seen the trick and those who haven't.
Here's the trick. Assume you have a piece of paper upon which is drawn the graph of the function of interest. To see what the graph of the inverse looks like:
1) Rotate the paper 90 degrees counter-clockwise.
2) Flip the paper over.
3) Hold the page up to a light so you can see through it.
Viola! You are now looking at the graph of the inverse of the function.
Want a handy diagram of the process? On a mug? Of course you do.
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