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70 POINTS!

{Questions 54 & 58}
The function f is one to one. Find to inverse. State the domain & the range of f & f^-1. Graph f & f^-1, & y=x on the same coordinate axes.

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70 POINTS! {Questions 54 & 58} The function f is one to one. Find to inverse. State-example-1
User Sciyoshi
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Notation

The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.

Inverses

A function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y.

A function f -1 is the inverse of f if

for every x in the domain of f, f -1[f(x)] = x, andfor every x in the domain of f -1, f[f -1(x)] = xThe domain of f is the range of f -1 and the range of f is the domain of f -1.Graph of the Inverse FunctionThe inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.Points on the identity function (y=x) will remain on the identity function when switched. All other points will have their coordinates switched and move locations.The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.
User Crlsrns
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