Inverse Functions – Inverse Functions

Inverse Functions

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The problems in this lesson cover inverse functions, or the inverse of a function, which is written as f-1(x), or 'f-1 of x.' To find the inverse of a function, such as f(x) = 2x - 4, think of the function as y = 2x - 4. Next, simply switch the x and the y, to get x = 2y - 4. Next, solve for y, and we have y = (1/2)x + 2. Finally, replace the y with f-1(x), or f-1 of x, and we have f-1(x) = (1/2)x + 2. Therefore, f(x) = 2x + 4 and f-1(x) = (1/2)x + 2 are inverse functions. In summary, when finding inverse functions, we replace the f(x) with y, switch the x and y, solve for y, then replace the y with f-1(x). When graphing inverse functions, it's important to understand that the graph a function and its inverse will be mirror images of each other in the line y = x. In this lesson, no inverse functions calculator is required, and a self-test serves as an interactive inverse functions worksheet.
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