Understanding the Inverse Function
In mathematics, the inverse of a function essentially reverses the operations of the original function. If you start with a function and then apply its inverse, you will retrieve your original value. For example, if we have a function defined as y = f(x), the inverse operation would be to express x = f-1(y). This holds true for one-to-one functions, where each output is produced by exactly one input.
Finding the Inverse of y = 3x
To find the inverse of the function y = 3x, we need to follow these steps:
- Swap the variables (x and y). This step involves rewriting the equation from y = 3x to x = 3y.
- Isolate y. To do this, we can divide both sides of the equation by 3:
y = x/3 - The expression obtained is the inverse function.
The Final Result
Therefore, the inverse of the function y = 3x is y = x/3 or, denoting the inverse function, f-1(x) = x/3.
This means that if we take the output of the original function (3x) and apply the inverse function (x/3), we will return to our initial input value of x.