![]() Properties of Inverse functions Inverse functions have the following properties: This rule occurs because a function and its inverse are a reflection of each other in the line y = □. We can see on the graph above, that the domain of the inverse function is equal to the range of the original function. The range of an inverse function is equal to the domain of the original function. The domain of an inverse function is equal to the range of the original function. The inverse function is a reflection of the original function in the line y = □. The inverse of this restricted function is now shown as. This portion of the graph is shown below, with no graph in the negative quadrants of the axes. The function is not a one-to-one function and so, to find its inverse, we must restrict the domain to □≥0 so that the function is one-to-one. The graph of the inverse function is a reflection of the original function in the line y = x. For any one-to-one function, f(x), there is an inverse function, written as f -1(x). What are Inverse Functions?Īn inverse function is a function which undoes the operation of the original function. ![]() This is just the notation used to indicate an inverse. f -1(□) does not mean to raise the function f(□) to the power of -1. The correct way to say this is ‘f inverse of □’. Instead of, we can write this as to indicate that this is the inverse function of f(□) = 5□ – 2.į -1(□) is the correct way to write the inverse of f(□). We start with the equation □ = 5y – 2 and add to to both sides to get □ + 2 = 5y. We want to rearrange the equation to get ‘y=’. We switch the □ for a y and the y for an □ so that the equation y = 5□ – 2 becomes □ = 5y – 2. Replace every x in the equation with a y and the y with an x ![]() ![]() Replace the ‘f(x)=’ in the equation with ‘y=’ Replace every x in the equation with a y and the y with an x.įor example, find the inverse function for f(□) = 5□ – 2.Replace the ‘f(x)=’ in the equation with ‘y=’.How to Find an Inverse Function To find an inverse function: ![]()
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