Previous Next


Example 2: Find the inverse of f (x) = , x≥2 (we must restrict the domain because f (x) is undefined for x < 2).

Original function:

  1. Subract 2.
  2. Take the square root.
New function:
  1. Square.
  2. Add 2.
Thus, f-1(x) = x2 + 2.

Check:
f-1(f (x)) = f-1() = ()2 + 2 = (x - 2) + 2 = x.
f (f-1(x)) = f (x2 +2) = = = x.

When we take the inverse of a function, the domain and range switch. In example 2, the domain of f is x≥2 and the range of f is f (x)≥ 0. Thus, the domain of f-1 is x≥ 0 and the range of f-1 is f-1(x)≥2.

Previous page Inverse Functions page 1 Next section

Take a Study Break