Question

Given f(x)=6+3sqrt(x-2), Find f^-1(x)=

Answer 1

To find the inverse of the function f(x) = 6 + 3√(x-2), interchange x and f(x), solve for x, and rewrite the equation in terms of x.

Step-by-step explanation:

To find the inverse of the function f(x) = 6 + 3√(x-2), we need to interchange x and f(x) and solve for x. Start by writing f(x) as y.

y = 6 + 3√(x-2)

Now, interchange x and y:

x = 6 + 3√(y-2)

Next, solve this equation for y:

y = ((x-6)/3)^2 + 2

Therefore, the inverse of f(x) is f-1(x) = ((x-6)/3)^2 + 2.