diketahui :
f(x) = 3x
g(x) = 5 - 2x
tentukan:
1. (fog) (x)
2. (fog) (5)
3. (gof) (x)
4. (gof) (10)
5. (fof) (x)
6. (fof) (20)
7. (gog) (x)
8. (gog) (3)

Let's solve the given problems step by step.

### Given Functions:
\[
f(x) = 3x
\]
\[
g(x) = 5 - 2x
\]

### 1. Find \((f \circ g)(x)\)
\[
(f \circ g)(x) = f(g(x))
\]
Substituting \(g(x)\):
\[
f(g(x)) = f(5 - 2x) = 3(5 - 2x) = 15 - 6x
\]
Thus,
\[
(f \circ g)(x) = 15 - 6x
\]

### 2. Find \((f \circ g)(5)\)
Using the result from the previous part:
\[
(f \circ g)(5) = 15 - 6(5) = 15 - 30 = -15
\]

### 3. Find \((g \circ f)(x)\)
\[
(g \circ f)(x) = g(f(x))
\]
Substituting \(f(x)\):
\[
g(f(x)) = g(3x) = 5 - 2(3x) = 5 - 6x
\]
Thus,
\[
(g \circ f)(x) = 5 - 6x
\]

### 4. Find \((g \circ f)(10)\)
Using the result from the previous part:
\[
(g \circ f)(10) = 5 - 6(10) = 5 - 60 = -55
\]

### 5. Find \((f \circ f)(x)\)
\[
(f \circ f)(x) = f(f(x))
\]
Substituting \(f(x)\):
\[
f(f(x)) = f(3x) = 3(3x) = 9x
\]
Thus,
\[
(f \circ f)(x) = 9x
\]

### 6. Find \((f \circ f)(20)\)
Using the result from the previous part:
\[
(f \circ f)(20) = 9(20) = 180
\]

### 7. Find \((g \circ g)(x)\)
\[
(g \circ g)(x) = g(g(x))
\]
Substituting \(g(x)\):
\[
g(g(x)) = g(5 - 2x) = 5 - 2(5 - 2x) = 5 - 10 + 4x = 4x - 5
\]
Thus,
\[
(g \circ g)(x) = 4x - 5
\]

### 8. Find \((g \circ g)(3)\)
Using the result from the previous part:
\[
(g \circ g)(3) = 4(3) - 5 = 12 - 5 = 7
\]

### Summary of Results
1. \((f \circ g)(x) = 15 - 6x\)
2. \((f \circ g)(5) = -15\)
3. \((g \circ f)(x) = 5 - 6x\)
4. \((g \circ f)(10) = -55\)
5. \((f \circ f)(x) = 9x\)
6. \((f \circ f)(20) = 180\)
7. \((g \circ g)(x) = 4x - 5\)
8. \((g \circ g)(3) = 7\)

Would you like more details or have any questions?

### 5 Related Questions
1. What is the definition of function composition in mathematics?
2. How do you interpret the meaning of \((f \circ g)(x)\) in real-world applications?
3. How can you determine whether the composition of two functions is commutative, i.e., whether \(f \circ g = g \circ f\)?
4. What happens when you compose more than two functions together, e.g., \((f \circ g \circ h)(x)\)?
5. How do inverses of functions relate to function composition?

### Tip
When composing functions, always substitute the inner function into the outer function carefully, and work step-by-step to avoid mistakes.

diketahui : f(x) = 3x g(x) = 5 - 2x tentukan: 1. (fog) (x) 2. (fog) (5) 3. (gof) (x) 4. (gof) (10) 5. (fof) (x) 6. (fof) (20) 7. (gog) (x) 8. (gog) (3)

Solve various function composition problems using the linear functions f(x) = 3x and g(x) = 5 - 2x. This tutorial covers how to compute (f ∘ g)(x), (g ∘ f)(x), (f ∘ f)(x), and (g ∘ g)(x), including step-by-step solutions for specific values. Suitable for Grades 9-11.

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