https://file.aiquickdraw.com/mathbot/file/1727194949381knmld4zg.jpg

From the image, the problem asks to determine the following based on given functions:

1. \( f(x) = \frac{x+1}{2} \) and \( g(x) = 2x - 3 \)
   
   a) \( f(g(x)) \)
   b) \( g(f(x)) \)

Let's solve them one by one:

### a) \( f(g(x)) \) (This represents \( f \circ g \), meaning apply \( g(x) \) first, then use \( f \) on the result)

We know:
- \( f(x) = \frac{x+1}{2} \)
- \( g(x) = 2x - 3 \)

Now, \( f(g(x)) \) means we substitute \( g(x) \) into \( f(x) \):

\[
f(g(x)) = f(2x - 3) = \frac{(2x - 3) + 1}{2}
\]

Simplify the expression inside:

\[
f(g(x)) = \frac{2x - 3 + 1}{2} = \frac{2x - 2}{2} = x - 1
\]

Thus:
\[
f(g(x)) = x - 1
\]

### b) \( g(f(x)) \) (This represents \( g \circ f \), meaning apply \( f(x) \) first, then use \( g \) on the result)

We know:
- \( f(x) = \frac{x+1}{2} \)
- \( g(x) = 2x - 3 \)

Now, \( g(f(x)) \) means we substitute \( f(x) \) into \( g(x) \):

\[
g(f(x)) = g\left( \frac{x+1}{2} \right) = 2\left( \frac{x+1}{2} \right) - 3
\]

Simplify the expression:

\[
g(f(x)) = (x+1) - 3 = x - 2
\]

Thus:
\[
g(f(x)) = x - 2
\]

### Final answers:
a) \( f(g(x)) = x - 1 \)

b) \( g(f(x)) = x - 2 \)

---

Would you like more details or further explanations?

Here are five related questions you could explore:
1. How do we determine the domain of composite functions like \( f(g(x)) \)?
2. What happens if the functions involve more complex expressions, like polynomials or trigonometric terms?
3. Can you find the inverse of \( f(x) \) and \( g(x) \)?
4. What is the composition of functions when \( f(x) \) and \( g(x) \) are exponential or logarithmic?
5. How would the composition of functions change if \( f(x) \) and \( g(x) \) involve absolute value expressions?

**Tip**: When working with composite functions, carefully substitute the inner function and simplify step-by-step.

Diketahui f(x) = (x + 1) / 2 dan g(x) = 2x - 3. Tentukan a) f(g(x)) b) g(f(x))

Learn how to find composite functions f(g(x)) and g(f(x)) for given linear functions f(x) = (x + 1) / 2 and g(x) = 2x - 3. Step-by-step solutions provided for high school algebra 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