I need help! Fin the inverse of the function, How do I work the below problem. I need an example do to all the examples I have all have an (fx, g or y) I am working 6 problems like this.
{(1, 0), (2, 1), (-1, 0), (-2, 0)}
There will not be an inverse for this function. Not all functions have inverses.
Notice f(x) is zero when x=anythign other than 2. So, the inverse (zero) cannot map back to a specific x.
There has to be a one to one correspondence both ways x->y and y->x for inverses to exist.
Now if it had been something like this,
(1,0); (3,-3); (34,17); (0,3) the inverse would have been
(0,1);-3,3; 17,34; 3,0
To find the inverse of a function, you need to swap the x and y values and then solve for y. In your case, you are given a set of points: {(1, 0), (2, 1), (-1, 0), (-2, 0)}. Let's go through the process step by step using one of the points as an example.
Let's take the point (1, 0). To find the inverse, we need to swap the x and y values. So, we have (0, 1). Now, we need to solve for y.
The inverse function will have the form y = f^(-1)(x), where f^(-1) denotes the inverse function. In this case, we want to solve for y.
The given points represent the original function, so we can say:
f(1) = 0
Now, in the inverse function, we need to solve for y when the x-value is 0. So, we have:
f^(-1)(0) = y
To find the value of y, we need to determine which value of x in the original function maps to y = 0. From the given points, we see that when x = 1, y = 0.
Therefore, the inverse function at x = 0 is y = 1.
Repeat this process for each given point, and you will find the inverse function. In your case, you need to perform this process for the remaining 5 points in order to determine the complete inverse function.