Explanation:
To find the inverse of an equation, we need to switch the roles of the dependent variable and the independent variable. In other words, if we have an equation of the form y = f(x), we need to rewrite it as x = f^{-1}(y), where f^{-1}(y) is the inverse function of f.
Once we have found the inverse equation, we can perform the original steps of the inverse equation by plugging in the output of the inverse function into the original equation.
For example, let's say we have the equation y = 2x + 3. To find the inverse equation, we first switch the roles of x and y to get:
x = 2y + 3
Next, we solve for y in terms of x:
x - 3 = 2y
(y = x - 3)/2
So the inverse equation is y = (x - 3)/2.
To perform the original steps of the inverse equation, we can plug the output of the inverse function, (x - 3)/2, into the original equation, y = 2x + 3:
y = 2((x - 3)/2) + 3
y = x - 3 + 3
y = x
We have arrived back at the independent variable, x, so the inverse and original steps have canceled each other out, as expected.