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Domain and range of inverse functions

Adapted from OpenStax Calculus Volume 11

Formula

domain and range of inverse functions

Since the inverse function reverses the original function, we have the following formulas for its domain and range:

  • Df−1=Rf
  • Rf−1=Df

Example

Question:
Find the domain and range of the function

f:x↦x+2,x∈ℝ,x≥−2.

Solution:

graph of square root of x+2

Df−1=Rf=[0,∞)∎
Rf−1=Df=[−2,∞)∎

  1. Content in this page is adapted from OpenStax Calculus Volume 1 by Gilbert Strang and Edwin “Jed” Herman under the Creative Commons Attribution Noncommercial Sharealike 4.0 License.
    Access for free at https://openstax.org/books/calculus-volume-1/pages/1-4-inverse-functions↩︎