Diketahuit f(x)=3x-1 dan g(x)=X²+3x+2
a. (fog) (x) 
b. (gof) (3)

Given two functions:

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

Let's find:

### a. \((fog)(x)\) or \( f(g(x)) \)
To find \( (fog)(x) \), we substitute \( g(x) \) into \( f(x) \).

1. First, identify \( g(x) = x^2 + 3x + 2 \).
2. Replace \( x \) in \( f(x) \) with \( g(x) \):  
\[
f(g(x)) = 3(g(x)) - 1
\]
3. Substitute \( g(x) \):  
\[
f(g(x)) = 3(x^2 + 3x + 2) - 1
\]
4. Simplify:  
\[
f(g(x)) = 3x^2 + 9x + 6 - 1
\]
\[
f(g(x)) = 3x^2 + 9x + 5
\]

So, \( (fog)(x) = 3x^2 + 9x + 5 \).

### b. \((gof)(3)\) or \( g(f(3)) \)
To find \( (gof)(3) \), we first calculate \( f(3) \) and then substitute it into \( g(x) \).

1. Calculate \( f(3) \):
\[
f(3) = 3(3) - 1 = 9 - 1 = 8
\]

2. Substitute \( f(3) = 8 \) into \( g(x) \):
\[
g(8) = 8^2 + 3(8) + 2
\]
\[
g(8) = 64 + 24 + 2 = 90
\]

So, \( (gof)(3) = 90 \).

Would you like more details, or do you have any questions?

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Here are 5 related questions to consider:

1. What would \((fog)(2)\) be for the same functions?
2. How would \((gof)(x)\) be derived for these two functions in general?
3. Can we find the inverse of \( f(x) \)? If so, what is it?
4. What is the domain of \( g(x) \) for which \((fog)(x)\) is defined?
5. How does \( (fog)(x) \) behave as \( x \) approaches infinity?

**Tip**: When evaluating compositions like \( f(g(x)) \), always substitute \( g(x) \) first and then simplify the expression step-by-step.

Diketahui f(x)=3x-1 dan g(x)=x²+3x+2. a. (fog)(x) b. (gof)(3)

Solve the function composition problem with f(x)=3x-1 and g(x)=x²+3x+2. Learn how to compute (fog)(x) and (gof)(3) using algebraic manipulation and function composition rules. Suitable for students in Grades 9-11.

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