ƒ¹(x) [constant]
In mathematics, the notation ƒ¹(x) is used to denote the inverse function of ƒ(x), where ƒ(x) is a given function
In mathematics, the notation ƒ¹(x) is used to denote the inverse function of ƒ(x), where ƒ(x) is a given function. The superscript ¹ represents the power of -1, which signifies the inverse function.
The inverse function of ƒ(x), denoted as ƒ⁻¹(x), essentially “undoes” the operations performed by the original function ƒ(x). This means that applying ƒ⁻¹(x) to the output of the original function ƒ(x) will return the original input value.
For example, if ƒ(x) = 2x, the inverse function ƒ⁻¹(x) will “undo” the multiplication by 2 and return the original value of x. In this case, ƒ⁻¹(x) = x/2.
The presence of a constant in the notation, as in ƒ¹(x) [constant], implies that the inverse function is defined for a specific constant value. This means that the inverse function will only “undo” the operations performed by the original function for a fixed value of the constant.
To illustrate this, let’s consider the function ƒ(x) = 2x + 3. The inverse function ƒ⁻¹(x) [constant] will “undo” the addition of 3 and the multiplication by 2. However, the constant value indicates that the inverse function is specifically defined for a certain constant. For instance, if the constant is given as 5, the inverse function ƒ⁻¹(x) [5] will be the function that “undoes” the operations and also subtracts 5 from the original value ƒ(x).
In summary, the notation ƒ¹(x) [constant] represents the inverse function of ƒ(x) with respect to a certain constant value.
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