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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]

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