<p>I found this question in Barron's SAT II math IIC book.
Q:(I am paraphrasing it) what is the inverse function of the f(x)=y?
I was stuck between either y=x or there is no inverse. What is the answer?</p>
<p>anyone here?</p>
<p>Any function f(x) = y simply says "Given a value of x, here's the computed value of y" . The inverse function g(y)=x works in reverse; " Given a value of y, here's a computed value of x which will give you f(x)=y".</p>
<p>If f(x) = 2x, for example, then the inverse function is g(y) = 0.5y .
If f(x) = x^2, then g(y) = sqrt(y) .</p>
<p>Without knowing the exact structure of f(x), I don't think it's possible to answer this problem. If f(x) = x, then the inverse function would be g(y) = y.</p>
<p>f(x)=x is it's own inverse. Since no change is done to x during the function, it is its own inverse, as in no inverse needed to reverse the function. </p>
<p>Graph y=x. Now graph another function and its inverse function. The 2 additional functions besides y=x are flipped across the y=x line. y=x sort of serves as the axis in which functions and their inverses are flipped relative to each other.</p>