Determine whether the function has an inverse function fx s

Determine whether the function has an inverse function. f(x) = squarerootx minus 6, x greaterthanorequalto 6 Yes, f does have an inverse. No, f does not have an inverse. If it does, find the inverse function. (If an answer does not exist, enter DNE.) f^minus1(x) =, x greaterthanorequalto 0

Solution

A function, f(x), has an inverse function if f(x) is one-to-one

f(x) = sqrt( x-6) has an inverse function as it is one-to-one function and it passes horizontal line test

Yes f does have an inverse

Find inverse :

Plug x= y and y =x and solve for x:

x= sqrt(y -6)

take square of both sides:

x^2 = y- 6

y = x^2 +6

f^-1(x) = x^2 +6