Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = \frac{1}{3} - \frac{1}{21}x$

Step 2: Find inverse

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