If f: R→ Rand g: R→ R defined by f(x) = 2x+1 and g(x) = 3x+1. (i) Find the functional values to the algebraic operations $$ \frac{f}{g} $$(x)

To find the functional values of the algebraic operation $\frac{f}{g}(x)$, where $ f(x) = 2x + 1 $ and $ g(x) = 3x + 1 $, we perform the following steps:

### Given Functions:
- $ f(x) = 2x + 1 $
- $ g(x) = 3x + 1 $

### Step-by-step Calculation:

The algebraic operation $\frac{f}{g}(x)$ is interpreted as:

\[
\frac{f}{g}(x) = \frac{f(x)}{g(x)}
\]

Now, substitute $ f(x) $ and $ g(x) $ into the equation:

\[
\frac{f}{g}(x) = \frac{2x + 1}{3x + 1}
\]

### Final Expression:

\[
\frac{f}{g}(x) = \frac{2x + 1}{3x + 1}
\]

This is the functional value for $\frac{f}{g}(x)$.

Would you like further clarification on this or any additional details?

Here are five related questions:
1. How would you find $ f \cdot g(x) $ for these functions?
2. What is the result of $ f + g(x) $?
3. Can you compute $ g - f(x) $?
4. How would you find the composition $ f(g(x)) $?
5. What is the inverse of $ f(x) = 2x + 1 $?

**Tip:** When dealing with functions, be mindful of the domain to ensure no values result in undefined expressions (such as division by zero).

If f: R→ R and g: R→ R defined by f(x) = 2x+1 and g(x) = 3x+1. (i) Find the functional values to the algebraic operations $$ \frac{f}{g} $$ (x)

Learn how to find the functional value of the algebraic operation $ \frac{f}{g}(x) $ where $ f(x) = 2x + 1 $ and $ g(x) = 3x + 1 $. This solution covers key concepts in functions and algebraic operations, ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation