It looks like you're trying to define two functions. Let me clarify the equations and provide you with the correct notation.

1. \( f(x) = x^2 - 1 \) 
   - This is a quadratic function.

2. \( g(x) = \frac{2}{x-1} \)
   - This is a rational function.

Would you like to combine these functions (such as finding \( (f \circ g)(x) \), \( (g \circ f)(x) \), or \( f(x) + g(x) \))? Or do you have a specific task in mind, such as solving or graphing them?

Here are five questions that can help expand this concept:

1. Would you like to find the sum \( f(x) + g(x) \)?
2. Should we compute the composition \( (f \circ g)(x) \) or \( (g \circ f)(x) \)?
3. Are you interested in solving for \( x \) when \( f(x) = g(x) \)?
4. Would you like to discuss the domain and range of each function?
5. Are you looking for the intercepts or critical points of these functions?

**Tip:** When combining functions, it's essential to carefully handle their domains to avoid undefined values (e.g., in \( g(x) \), \( x = 1 \) is not allowed).

Explore how to analyze and combine the quadratic function f(x) = x^2 - 1 and the rational function g(x) = 2/(x-1). Learn about function composition, solving equations, and handling undefined values in rational functions. Suitable 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