Question

The function of f (x) is defined by f (x)=4x+7. the inverse of f (x) is g (x). what is g (15)?

Answer 1

Answer:

g(15) = 2

General Formulas and Concepts:

Pre-Alg

• Order of Operations: BPEMDAS
• Equality Properties

Algebra I

• Function inverses

Step-by-step explanation:

Step 1: Define

f(x) = 4x + 7

g(x) = f⁻¹(x)

g(15) is x = 15

Step 2: Find inverse

1. Rewrite:                    y = 4x + 7
2. Swap:                        x = 4y + 7
3. Isolate y term:          x - 7 = 4y
4. Isolate y:                   (x - 7)/4 = y
5. Rewrite:                    y = (x - 7)/4
6. Back-substitute:       g(x) = (x - 7)/4

Step 3: Evaluate

1. Substitute:                    g(15) = (15 - 7)/4
2. Subtract:                       g(15) = 8/4
3. Divide:                          g(15) = 2