https://file.aiquickdraw.com/mathbot/file/172705757484465udul77.jpg

Let's break down the problem step by step.

We are given the functions:

- \( f(x) = \sqrt{x} \)
- \( g(x) = x + 6 \)

We are tasked with finding the following:

### a. \( (f \circ g)(x) \)
This means we need to compute the composition of \( f \) and \( g \), which is \( f(g(x)) \). 

1. First, substitute \( g(x) = x + 6 \) into \( f(x) \).
2. \( f(g(x)) = f(x + 6) = \sqrt{x + 6} \)

Thus, \( (f \circ g)(x) = \sqrt{x + 6} \).

---

Let me know if you'd like details for the other parts (b, c, and d), and if you have any questions!

Here are 5 related questions for practice:
1. How do you evaluate \( (g \circ f)(x) \)?
2. What is the value of \( (f \circ g)(3) \)?
3. How do you calculate \( (g \circ f)(3) \)?
4. What is the domain of the function \( (f \circ g)(x) \)?
5. How do you interpret function composition in real-world applications?

**Tip:** When composing functions, always substitute the inner function first before applying the outer function.

For f(x) = √x and g(x) = x + 6, find the following functions: (f ∘ g)(x), (g ∘ f)(x), (f ∘ g)(3), and (g ∘ f)(3).

Learn how to find the composition of functions where f(x) = √x and g(x) = x + 6. Includes solutions for (f ∘ g)(x), (g ∘ f)(x), (f ∘ g)(3), and (g ∘ f)(3). Suitable for students in Grades 10-12 studying function operations and composition.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation