Given Function : f(x)= squrt (x-3) Determine the inverse and state is the inverse is a function.Please justify your answer.

Expert Answers
rugbykats eNotes educator| Certified Educator

f(x) = squrt (x-3)

Replace f(x) with y:

y = squrt (x-3)

Replace each y with x and each x with y:

x = squrt (y-3)

Solve for y:

x^2 = y - 3

y = x^2 + 3

Replace the y with f[-1]:

f[-1](x) = x^2 + 3

Since every x value produces a unique y value, it is indeed a function.

Hope this helps. Good luck!