Consider the function for the domain

Question

Consider the function f(x)= ⎷4-x   +2  for the domain

(-infinity, 4]

Find f^-1(x), where f^-1 is the inverse of f

Also, state the domain f^-1 in interval notation. 

 

Answer 1

y=√(x-4)+2 

(y-2)²=x-4

(y-2)²+4=x

 

So f^-1(x)=(x-2)²+4

Domain whole  real axis