Examples of inverse function in the following topics:
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- An inverse function is a function that undoes another function: For a function $f(x)=y$ the inverse function, if it exists, is given as $g(y)= x$.
- Inverse function is a function that undoes another function: If an input $x$ into the function $f$ produces an output $y$, then putting $y$ into the inverse function $g$ produces the output $x$, and vice versa. i.e., $f(x)=y$, and $g(y)=x$.
- A function $f$ that has an inverse is called invertible; the inverse function is then uniquely determined by $f$ and is denoted by $f^{-1}$ (read f inverse, not to be confused with exponentiation).
- Not all functions have an inverse.
- A function $f$ and its inverse $f^{-1}$.
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- An inverse function is a function that undoes another function.
- A function $f$ that has an inverse is called invertible; the inverse function is then uniquely determined by $f$ and is denoted by $f^{-1}$.
- Stated otherwise, a function is invertible if and only if its inverse relation is a function on the range $Y$, in which case the inverse relation is the inverse function.
- Not all functions have an inverse.
- A function $f$ and its inverse, $f^{-1}$.
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- It is useful to know the derivatives and antiderivatives of the inverse trigonometric functions.
- The inverse trigonometric functions are also known as the "arc functions".
- There are three common notations for inverse trigonometric functions.
- They can be thought of as the inverses of the corresponding trigonometric functions.
- The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions.
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- A continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output.
- A continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output.
- Otherwise, a function is said to be a "discontinuous function."
- A continuous function with a continuous inverse function is called "bicontinuous."
- This function is continuous.
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- Hyperbolic function is an analog of the ordinary trigonometric function, also called circular function.
- The basic hyperbolic functions are the hyperbolic sine "$\sinh$," and the hyperbolic cosine "$\cosh$," from which are derived the hyperbolic tangent "$\tanh$," and so on, corresponding to the derived functions.
- The inverse hyperbolic functions are the area hyperbolic sine "arsinh" (also called "asinh" or sometimes "arcsinh") and so on.
- The hyperbolic functions take real values for a real argument called a hyperbolic angle.
- When considered defined by a complex variable, the hyperbolic functions are rational functions of exponentials, and are hence meromorphic.
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- Exponential function is the function $e^x$ the number (approximately 2.718281828) such that the function $e^x$ is its own derivative .
- Sometimes the term exponential function is used more generally for functions of the form $f(x)=cb^x$, where the base $b$ is any positive real number and $c$ is a constant.
- The exponential function $e^x$ can be characterized in a variety of equivalent ways.
- For $f(x)=e^x$, $g(x)=\log_e(x)$ is the inverse function of $f(x)$ and vice versa.
- The derivative (or slope of a tangential line) of the exponential function is equal to the value of the function.
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- Now that we have derived a specific case, let us extend things to the general case of exponential function.
- Here we consider integration of natural exponential function.
- Note that the exponential function $y = e^{x}$ is defined as the inverse of $\ln(x)$.
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- Integration is the process of finding the region bounded by a function; this process makes use of several important properties.
- Integration is an important concept in mathematics and—together with its inverse, differentiation—is one of the two main operations in calculus.
- The term integral may also refer to the notion of the anti-derivative, a function $F$ whose derivative is the given function $f$.
- Given two functions $f(x)$ and $g(x)$, we can use the following identity:
- A definite integral of a function can be represented as the signed area of the region bounded by its graph.
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- Integration is an important concept in mathematics and—together with its inverse, differentiation—is one of the two main operations in calculus.
- We ask, "What is the area under the function $f$, over the interval from 0 to 1?
- Notice that we are taking a finite sum of many function values of $f$, multiplied with the differences of two subsequent approximation points.
- A definite integral of a function can be represented as the signed area of the region bounded by its graph.
- Compute the definite integral of a function over a set interval
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- Integration is an important concept in mathematics and—together with its inverse, differentiation—is one of the two main operations in calculus.
- We ask, "What is the area under the function $f$, over the interval from $0$ to $1$?
- Notice that we are taking a finite sum of many function values of $f$, multiplied with the differences of two subsequent approximation points.
- However, you can also use integrals to calculate length—for example, the length of an arc described by a function $y = f(x)$.
- A definite integral of a function can be represented as the signed area of the region bound by its graph.