Question

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

Answer 1

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

Answer 2

f⁻¹(x) = (x + 10)/2

General Formulas and Concepts:

Algebra I

• Equality Properties
• Inverse Functions

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