I need help with an inverse function. If f(x)=3-x, I find the inverse function to be: x=3-y which is the same as y=3-x, same as the original. How can this be?
Did you realize that
f(x) = 3-x is the same as
x + y = 3 ?
Step one in finding the inverse is to interchange the x and y variables, and lo and behold you would get
y + x = 3, which of course is the same as the one you started with.
Another explanation:
After finding the inverse, the resulting graph is a reflection in the line y = x
graph y = 3 - x, and you will see that reflecting it in the line y = x yields the same line.
Thanks!
To find the inverse of a function, you need to swap the roles of the dependent variable (y) and the independent variable (x). The inverse function will have the variables switched, with the dependent variable (y) as the new independent variable and the independent variable (x) as the new dependent variable.
Let's see how this works with the given function f(x) = 3 - x:
1. Start with the original function, f(x) = 3 - x.
2. Replace f(x) with y: y = 3 - x.
3. Swap x and y: x = 3 - y.
4. Solve the equation for y: y = 3 - x.
At first glance, it may seem like the inverse function is the same as the original function, but it actually isn't. The reason is that when you graph both the original and inverse functions, you'll notice that they are reflections of each other across the line y = x.
So, both f(x) = 3 - x and its inverse function y = 3 - x are correct representations of each other. This is because when you compose the original function with its inverse, they "undo" each other, resulting in the input value you initially started with.