Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Functions
An inverse function, denoted as f¯¹(x), reverses the effect of the original function f(x). For a function to have an inverse, it must be one-to-one, meaning each output is produced by exactly one input. To find the inverse, you typically swap the x and y variables in the equation and solve for y.
Recommended video:
Graphing Logarithmic Functions
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 reflections of each other across the line y = x. This visual representation helps in understanding how the function and its inverse interact.
Recommended video:
Graphs of Logarithmic Functions
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. Using interval notation, we can succinctly express these sets, which is essential for understanding the behavior of the functions.
Recommended video:
Domain & Range of Transformed Functions