For the given​ functions, find ​(fcircle​g)(x) and ​(gcircle​f)(x) and the domain of each.
​f(x)equalsx squaredplus3​, ​ g(x)equalsStartRoot 5 minus x EndRoot
Question content area bottom
Part 1
​(fcircle​g)(x)equals

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

### Step 1: Write the given functions
- \( f(x) = x^2 + 3 \)
- \( g(x) = \sqrt{5 - x} \)

### Step 2: Substitute \( g(x) \) into \( f(x) \)
\[
(f \circ g)(x) = f(g(x)) = f\left(\sqrt{5 - x}\right)


For the given functions, find (f ∘ g)(x) and (g ∘ f)(x) and the domain of each.
f(x) = x^2 + 3, g(x) = √(5 - x)

Explore function composition and domain determination for f(x) = x^2 + 3 and g(x) = √(5 - x). Learn to compute (f ∘ g)(x) and (g ∘ f)(x) step-by-step, including restrictions due to square root and quadratic functions. Ideal for Grades 9-12 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