Final answer:
To find the inverse function of f(x) = 6 - 3√x, switch the roles of x and y, solve for y, and rewrite the function as g(x) = (6 - x)^3/27.
Step-by-step explanation:
To find the inverse function of f(x) = 6 - 3√x, we need to switch the roles of x and y and solve for y. Let's start by rewriting the function:
y = 6 - 3√x
Now, let's switch x and y:
x = 6 - 3√y
Next, let's isolate √y:
3√y = 6 - x
To get rid of the cube root, we need to cube both sides:
(3√y)^3 = (6 - x)^3
Now, simplify both sides:
y = (6 - x)^3/27
Therefore, the inverse function of f(x) = 6 - 3√x is g(x) = (6 - x)^3/27.