Inverse function
SAT glossary · Course Foundations
Definition
f^-1 undoes f, so f(f^-1(x))=x; find it by swapping x and y and solving for y, and graphically it is f reflected over the line y=x. The superscript -1 is notation, not an exponent — f^-1(x) ≠ (1)/(f(x)), and the reciprocal is offered as a distractor.
Inverse function in plain English
An inverse function, written f^-1, is a function that perfectly UNDOES whatever the original function f did — feed f^-1 the output of f, and you get your original input right back, which is exactly what f(f^-1(x))=x means. To actually find one, swap the roles of x and y in the function's equation and then solve for the new y. Graphically, an inverse function is just the original graph flipped across the diagonal line y=x. One huge warning: that little -1 up top is just LABELING notation meaning 'the inverse function' — it is NOT an exponent, so f^-1(x) does not equal (1)/(f(x)) (the reciprocal), even though that reciprocal is exactly the wrong answer choice waiting to trap you.
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