Question content area top
Part 1
Let ​f(x)equals3xminus1 and ​g(x)equalsx squarednegative 1.
Find ​(fcircle​g)(0​).

We are given the functions \( f(x) = 3x - 1 \) and \( g(x) = x^2 - 1 \). We are tasked with finding \( (f \circ g)(0) \), which is the composition of \( f \) and \( g \) at \( x = 0 \).

### Step-by-step solution:

1. **Composition of functions:**  
   \( (f \circ g)(x) = f(g(x)) \), meaning we first evaluate \( g(x) \) and then substitute the result into \( f(x) \).

2. **Find \( g(0) \):**  
   Since \( g(x) = x^2 - 1 \), substituting \( 0 \) into \( g(x) \):
   \[
   g(0) = 0^2 - 1 = -1
   \]

3. **Evaluate \( f(g(0)) \):**  
   Now, we substitute \( g(0) = -1 \) into \( f(x) \). Since \( f(x) = 3x - 1 \), we calculate:
   \[
   f(-1) = 3(-1) - 1 = -3 - 1 = -4
   \]

Thus, \( (f \circ g)(0) = -4 \).

### Final Answer:
\[
(f \circ g)(0) = -4
\]

Would you like further details or have any questions?

---

Here are 5 related questions to expand your understanding:
1. What is \( (g \circ f)(0) \) for the same functions \( f(x) = 3x - 1 \) and \( g(x) = x^2 - 1 \)?
2. How would you find \( (f \circ g)(1) \)?
3. Can you compute \( (f \circ f)(0) \)?
4. What is the domain of \( f \circ g \)?
5. How does the composition of functions differ from addition of functions?

**Tip:** When working with compositions, always evaluate the inner function first!

Let f(x) = 3x - 1 and g(x) = x^2 - 1. Find (f ∘ g)(0).

Learn how to solve the function composition problem (f ∘ g)(0), where f(x) = 3x - 1 and g(x) = x^2 - 1. This problem explores key concepts in function composition and algebra, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation