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In this section, you will learn how to find the derivative of a function as a new function and how to use it to analyze the behavior of the original function. You will also see how the graphs of a function and its derivative are related. This is a key skill for calculus students and a prerequisite for the next topics. To learn more, visit the Mathematics LibreTexts website.
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To calculate the inverse of a function, swap the x and y variables then solve for y in terms of x. What are the 3 methods for finding the inverse of a function? There are 3 methods for finding the inverse of a function: algebraic method, graphical method, and numerical method.
Here we have the function f(x) = 2x+3, written as a flow diagram: The Inverse Function goes the other way: So the inverse of ... (less than or equal to 0) the inverse is then f-1 (x) = −√x: {x 2 | x ≤ 0 } {−√x | x ≥ 0 } Which are inverses, too. Not Always Solvable! It is sometimes not possible to find an Inverse of a Function ...
A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions.
the factored expression is ( x + 2) ( x − 5) . The complete solution of the equation would go as follows: x 2 − 3 x − 10 = 0 ( x + 2) ( x − 5) = 0 Factor. ↙ ↘ x + 2 = 0 x − 5 = 0 x = − 2 x = 5. Now it's your turn to solve a few equations on your own. Keep in mind that different equations call for different factorization methods.
If this is new to you, we recommend that you check out our end behavior of polynomials article. The zeros of a function f correspond to the x -intercepts of its graph. If f has a zero of odd multiplicity, its graph will cross the x -axis at that x value. If f has a zero of even multiplicity, its graph will touch the x -axis at that point.
