Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Functions
An inverse function reverses the effect of the original function. For a function f(x), its inverse f¯¹(x) satisfies the condition f(f¯¹(x)) = x for all x in the domain of f¯¹. To find the inverse, one typically swaps the roles of x and y in the equation and solves for y.
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Graphing Functions
Graphing functions involves plotting points on a coordinate system to visualize the relationship between the input (x) and output (f(x)). When graphing both a function and its inverse, the two graphs will be symmetric with respect to the line y = x, illustrating how each function undoes the other.
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Domain and Range
The domain of a function is the set of all possible input values (x) for which the function is defined, while the range is the set of all possible output values (f(x)). For inverse functions, the domain of f becomes the range of f¯¹, and vice versa. Interval notation is a concise way to express these sets, using brackets and parentheses to indicate whether endpoints are included.
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