Diketahuit f(x)=X² dan g(x)=X-5
a. (fog) (x) 
b. (gof) (3)

Given the functions \( f(x) = x^2 \) and \( g(x) = x - 5 \), let's solve the problems step by step.

### Part a: \( (f \circ g)(x) \)

The notation \( (f \circ g)(x) \) represents the composition of \( f \) and \( g \), meaning \( f(g(x)) \). This means we will substitute \( g(x) \) into the function \( f(x) \).

1. \( g(x) = x - 5 \)
2. Now substitute \( g(x) \) into \( f(x) \):
   \[
   f(g(x)) = f(x - 5) = (x - 5)^2
   \]
3. Simplify the expression:
   \[
   (x - 5)^2 = x^2 - 10x + 25
   \]
So, \( (f \circ g)(x) = x^2 - 10x + 25 \).

### Part b: \( (g \circ f)(3) \)

The notation \( (g \circ f)(3) \) represents the composition \( g(f(3)) \), meaning we will first find \( f(3) \), and then substitute that into \( g(x) \).

1. First, calculate \( f(3) \):
   \[
   f(3) = 3^2 = 9
   \]
2. Now, substitute \( f(3) = 9 \) into \( g(x) \):
   \[
   g(9) = 9 - 5 = 4
   \]
So, \( (g \circ f)(3) = 4 \).

---

Would you like further details on these steps, or do you have any questions?

### Related Questions:
1. What is \( (g \circ f)(x) \) for any \( x \)?
2. Can you expand \( (x - 5)^2 \) using another method?
3. What happens when \( f(x) \) and \( g(x) \) are different types of functions (e.g., exponential or trigonometric)?
4. How do you differentiate \( (f \circ g)(x) \)?
5. What are the domain and range of \( (f \circ g)(x) \)?

### Tip:
When performing composition of functions, always be careful with the order in which you substitute functions. \( f(g(x)) \) is not the same as \( g(f(x)) \).

Diketahui f(x)=X² dan g(x)=X-5
a. (fog)(x)
b. (gof)(3)

Learn how to solve function compositions for f(x) = x² and g(x) = x - 5, including detailed steps for calculating (fog)(x) and (gof)(3). This problem covers key algebraic concepts and function composition, 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