Introduction to the Composition of Functions and Inverse of a Function

# Introduction to the Composition of Functions and Inverse of a Function

## Composite and Inverse Functions

A composite function is a function that is composed of two or more functions. The composite function is created by combining the individual functions into one function. The composite function operates on the same inputs as the individual functions and produces the same outputs.

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The inverse function is a function that “undoes” the effect of another function. The inverse function is created by reversing the input and output of the original function. The inverse function operates on the same inputs as the original function and produces the same outputs.

### Composition of Functions

A function is a set of ordered pairs, where each element in the set corresponds to a unique output. The function can be represented using a graph, where the input is on the x-axis and the output is on the y-axis. The function will have a slope that corresponds to the rate of change between the input and output. The function will also have a y-intercept, which is the point where the function crosses the y-axis.

### Inverse Functions

An inverse function is a function that “undoes” another function. For example, the inverse of the function f(x) = x2 is the function g(x) = x.

To find the inverse of a function, we first need to determine its function’s inverse function’s domain and range. The inverse function’s domain is the set of all x-values for which the original function produces a valid result. The inverse function’s range is the set of all y-values for which the original function produces a valid result.

Next, we need to determine the function’s inverse function’s equation. The inverse function’s equation is the equation that “undoes” the original function. For example, the inverse function’s equation for the function f(x) = x2 is the equation g(x) = x.

Finally, we need to graph the inverse function. The inverse function’s graph is the mirror image of the original function’s graph.