You are asked to find \( f(g(x)) \) where:

- \( f(x) = 3x - 5 \)
- \( g(x) = 2x^2 - 5 \)

To find \( f(g(x)) \), we will substitute \( g(x) \) into \( f(x) \).

### Steps:
1. First, recall that \( f(x) = 3x - 5 \).
2. Replace \( x \) in \( f(x) \) with \( g(x) \):
   \[
   f(g(x)) = 3(2x^2 - 5) - 5
   \]
3. Now simplify the expression:
   \[
   f(g(x)) = 3(2x^2 - 5) - 5 = 6x^2 - 15 - 5
   \]
   \[
   f(g(x)) = 6x^2 - 20
   \]

Thus, \( f(g(x)) = 6x^2 - 20 \).

Would you like more details on the steps or explanations?

Here are five related questions:
1. How do you find \( g(f(x)) \)?
2. What is the general method for solving composite functions?
3. How would you determine the domain of \( f(g(x)) \)?
4. Can composite functions be inverse functions of each other?
5. How can we graph \( f(g(x)) \)?

**Tip:** Always simplify composite functions step-by-step to avoid mistakes.

F(x) = 3x - 5, g(x) = 2x² - 5: find f(g(x))

Learn how to solve the composite function f(g(x)) where f(x) = 3x - 5 and g(x) = 2x² - 5. Follow a detailed step-by-step explanation to simplify the expression and get f(g(x)) = 6x² - 20. This problem involves key concepts of composite functions and quadratic equations, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation