what is the inverse of the linear parent function?
How would you graph the inverse and what are the values for the inverse???
The inverse of the linear parent function is a function that reverses the input and output values of the original linear function. In other words, if the linear parent function is f(x) = mx + b, then its inverse is denoted as f^-1(x), and it can be represented as x = my + b.
To graph the inverse of a linear function, you can follow these steps:
1. Start with the graph of the linear parent function.
2. Identify a few points on the original function, such as (x1, y1), (x2, y2), etc.
3. Swap the x and y coordinates for each point to obtain the corresponding points on the inverse function, i.e., (y1, x1), (y2, x2), etc.
4. Plot these new points on a graph.
5. Connect the points with a smooth, continuous line.
The values for the inverse function will depend on the values of the original linear function. For example, if the original function is f(x) = 2x + 3, then the inverse function would be f^-1(x) = (x - 3)/2. The values of the inverse function will differ from those of the original function.
The linear parent function is written as f(x) = x. To find the inverse of this function, we need to swap the variables x and y and solve for y.
So, we start with the equation:
y = x
To find the inverse, we swap x and y:
x = y
Now, solving for y, we get:
y = x
As you can see, the inverse of the linear parent function is also the linear parent function itself. This means that the inverse is identical to the original function.
To graph the inverse of a linear function, you can simply graph the original linear function and then swap the x and y coordinates of each point. For example, if you have a point (3, 4) on the graph of the linear function, the corresponding point on the inverse function would be (4, 3).
The key idea here is that the graph of the linear function and its inverse are mirror images of each other across the line y = x. This is because swapping the x and y coordinates reflects the points across this line.
Since the inverse of the linear parent function is the linear parent function itself, the values for the inverse will be the same as the values for the original function. The x and y coordinates of the points on the graph of the inverse will be the same as the x and y coordinates of the corresponding points on the original graph.