If the graphs of y=f ^-1(x) and y=f(x) are identical then each of these graphs must be symmetrical about the
A)y-axis B)X-axis c)origin d)line y=-x e)line y=x
Note to anyone freaking out: this is NOT an SAT question. I assume it’s from a practice Subject Test?
The simplest case where is . That’s a graph we’re all familiar with, and it’s not symmetrical across either axis, so cross off A and B. The line is symmetrical about itself (I think?), so we’ll keep E for now, and we have to keep C and D, too.
Now, are there any, ONLY SLIGHTLY MORE COMPLICATED functions that equal their inverses? How about something like . In that case, to find the inverse, we flip and .
So if we graph , we see it’s not symmetrical about the origin or the line. It is still symmetrical about the line, though.