Inverse Function: How to Find the Value of g^-1(-2) with g(5)=-2

In summary, the conversation is about finding the inverse of a function when given a specific value. The concept of inverse functions is discussed, emphasizing that if a function maps b to a, then its inverse maps a to b. Two simplified formulations of inverse functions are also provided to aid in understanding. The final conclusion is that the inverse of g when g(5)=-2 is g^-1(-2)=5.
  • #1
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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
 
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  • #2
The most fundamental concept about a function that has an inverse is that if a = f(b),
then b = f-1(a). Use this concept in your problem.

In different words, f maps b to a, so f-1 is a pairing in the other direction; IOW, f-1 maps a to b.
 
  • #3
Think about these (very loose, incredibly non-mathematical) formulations of inverse functions.

"The inverse function reverses what the original function does."

"If you start at an x, apply the function to get a y, then apply the inverse function, you get back to x."

Does either of these help?
 

1. What is an inverse function?

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.

2. How do you find the inverse of a function?

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).

3. What does g^-1(-2) represent?

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.

4. How do you find the value of g^-1(-2) if g(5)=-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.

5. Can there be more than one inverse function for a given function?

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.

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