For 
f(x) = 6/x^3
 find and simplify the following.
f(x) − 7 =

We are given the function \( f(x) = \frac{6}{x^3} \), and we are asked to find \( f(x) - 7 \).

### Step-by-Step Solution:

1. First, write down \( f(x) - 7 \):
   \[
   f(x) - 7 = \frac{6}{x^3} - 7
   \]

2. To combine these two terms, express \( 7 \) as a fraction with a denominator of \( x^3 \):
   \[
   7 = \frac{7x^3}{x^3}
   \]

3. Now subtract the two fractions:
   \[
   \frac{6}{x^3} - \frac{7x^3}{x^3} = \frac{6 - 7x^3}{x^3}
   \]

Thus, the simplified expression is:
\[
f(x) - 7 = \frac{6 - 7x^3}{x^3}
\]

Would you like more details or have any questions about this process?

Here are 5 related questions:
1. How do you find the domain of \( f(x) - 7 \)?
2. What happens to the function as \( x \) approaches 0?
3. How would you differentiate \( f(x) - 7 \)?
4. Can you simplify the expression further for specific values of \( x \)?
5. How do you find the inverse of the function \( f(x) - 7 \)?

**Tip:** Always check for common factors in the numerator and denominator when simplifying rational expressions!

For f(x) = 6/x^3, find and simplify the following: f(x) − 7.

Discover how to simplify the function f(x) = 6/x^3 by subtracting 7 and expressing the result as a single rational expression. This solution covers key algebraic concepts such as rational expressions and operations with fractions, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation