Replace f(x) with y, exchange x and y, and then solve for y.
Inverse Function: f^(-1)=x-12/2 Explanation: See solution.
Practice makes perfect
We are asked to find the inverse for the given function. To do this, we will start with replacing f(x) with y.
f(x)=2x+12 ⇒ y=2 x+12
Next, to algebraically determine the inverse of the given equation we exchange x and y and solve for y.
Given Equation & Inverse Equation
y=2 x+12 & x=2 y+12
Finally, the result of isolating y in the new equation will be the inverse of the given function.
We ended with the inverse of the given function. Now we can replace y with f^(-1)(x).
f^(-1)=x-12/2
Since the original function represents the cost of pizza with the given number of toppings, the inverse function represents the number of toppings with the given cost of pizza.
