List the domain and range of the function fx then find the i

List the domain and range of the function f(x), then find the inverse function f1(x) and list its domain and range. f(x)=sqrt(36x)

Solution

f(x) = sqrt(3 - 6x)
Domain for f(x) : x <= 1/2

To find the Inverse function:

Let y = sqrt(3 - 6x)
Squaring both sides we get
y² = 3 - 6x
y² + 6x = 3
6x = 3 - y2
x = (3 - y2) / 6
Now we will replace y and x, we get

y = (3 -x²) / 6
f-1(x) = (3 - x²) / 6

Domain for Inverse function is f-1(x) : - infinity <x < infinity