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 f(x)=f^-1(x) is f(x)=x. That’s a graph we’re all familiar with, and it’s not symmetrical across either axis, so cross off A and B. The y=x 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 f(x)=5-x. In that case, to find the inverse, we flip x and y.




So if we graph y=5-x, we see it’s not symmetrical about the origin or the y=-x line. It is still symmetrical about the y=x line, though.

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