find the inverse of fxsqrtxh find the domain and range of th

find the inverse of f(x)=sqrt(x-h) find the domain and range of the inverse

Solution

f(x)=sqrt(x-h)

domain of f(x)=sqrt(x-h) is [h,infinity) , range is [0, infinity)

let y =f(x)

=> x= f^-1(y)

y=sqrt(x-h)

==>x-h=y²

=>x=h+y²

f^-1(y)=h+y²

f^-1(x)=h+x²

inverse of f(x)=sqrt(x-h) is f^-1(x)=h+x²

domain of f^-1(x)=h+x² is [0, infinity) , range is [h,infinity)