Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

What is the inverse of the function f(x) = 2x - 10?

Sagot :

Space

Answer:

f⁻¹(x) = (x + 10)/2

General Formulas and Concepts:

Algebra I

  • Equality Properties
  • Inverse Functions

Step-by-step explanation:

Step 1: Define

f(x) = 2x - 10

Step 2: Rewrite

  1. Redefine:                          y = 2x - 10
  2. Swap x/y:                          x = 2y - 10

Step 3: Find Inverse

Solve for the new y.

  1. Add 10 to both sides:                    x + 10 = 2y
  2. Divide 2 on both sides:                (x + 10)/2 = y
  3. Rewrite:                                          y = (x + 10)/2
  4. Redefine:                                       f⁻¹(x) = (x + 10)/2

Answer:

[tex]let \: the \: {f}^{ - 1}(x) \: be \: m \\ m = \frac{1}{2x - 10} \\ m(2x - 10) = 1 \\ 2x - 10 = \frac{1}{m} \\ x = \frac{1}{2m} + 5 \\ therefore \\ {f}^{ - 1} (x) = \frac{1}{2x} + 5[/tex]

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.