Question

Find the inverse of function f. f(x)=1/3 - 1/21x

Answer 1

A.
`\displaystyle f^(-1)(x) = 7 - 21x`

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Distributive Property

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Algebra I

• Terms/Coefficients
• Functions
• Function Notation
• Inverse Functions

Explanation:

Step 1: Define

Identify

`\displaystyle f(x) = (1)/(3) - (1)/(21)x`

Step 2: Find inverse

1. Rewrite:
   `\displaystyle y = (1)/(3) - (1)/(21)x`
2. Swap:
   `\displaystyle x = (1)/(3) - (1)/(21)y`
3. [Subtraction Property of Equality] Isolate y term:
   `\displaystyle x - (1)/(3) = -(1)/(21)y`
4. [Multiplication Property of Equality] Isolate y:
   `\displaystyle -21(x - (1)/(3)) = y`
5. [Distributive Property] Distribute -21:
   `\displaystyle 7 - 21x = y`
6. Rewrite:
   `\displaystyle f^(-1)(x) = 7 - 21x`