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Homework Statement
if g(5)=-2, then g^-1(-2)=?
Homework Equations
n/a
The Attempt at a Solution
i can't remember how to work inverse functions when there is no variable
i think its g^-1(-2)=5 but it could be g^-1(-2)=-2
An inverse function is a function that "undoes" the original function. It takes the output of the original function and returns the input value. In other words, if f(x) is the original function, then the inverse function is denoted as f^-1(x) and f^-1(f(x))=x.
To find the inverse of a function, follow these steps:1. Replace f(x) with y.2. Swap the x and y variables.3. Solve for y.4. Replace y with f^-1(x).The resulting function is the inverse function, f^-1(x).
g^-1(-2) represents the input value of the inverse function g^-1(x) when the output is -2. In other words, it is the value of x for which g(x)=-2.
If g(5)=-2, then the inverse function will have an input value of 5 when the output is -2. Therefore, g^-1(-2)=5.
No, there can only be one inverse function for a given function. However, some functions may not have an inverse function because they are not one-to-one, meaning that one input value can have multiple output values. In these cases, the inverse function does not exist.