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Rzqust [24]
3 years ago
15

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

Mathematics
2 answers:
Delicious77 [7]3 years ago
8 0

Answer:

f⁻¹(x) = (x + 10)/2

General Formulas and Concepts:

<u>Algebra I</u>

  • Equality Properties
  • Inverse Functions

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = 2x - 10

<u>Step 2: Rewrite</u>

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

<u>Step 3: Find Inverse</u>

<em>Solve for the new y.</em>

  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
Svetllana [295]3 years ago
7 0

Answer:

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

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