find a suitable restriction on the domain so that fx x22 is

find a suitable restriction on the domain so that f(x) = (x-2)² is one to one then find the inverse on that restricted domain

Solution

f(x)= (x-2)^2

To find the inverse , we have to put a restriction like x>2

And in that case inverse

f(x)=(x-2)^2

y=(x-2)²

x=(y-2)²

sqrt x= y-2

y= sqrtx +2

f^-1(x) =sqrtx + 2