diket=f(x)=x+4  g(x)=2-x  h(x)=x²-x+1.tentukan fungsi (fo(goh)(x)?

We are asked to find the composition of functions \( f \circ (g \circ h)(x) \), where:

- \( f(x) = x + 4 \),
- \( g(x) = 2 - x \),
- \( h(x) = x^2 - x + 1 \).

Let's break it down step by step:

### Step 1: Find \( (g \circ h)(x) \)
The function \( g \circ h(x) \) means \( g(h(x)) \), or applying \( g \) to \( h(x) \). 

Since \( h(x) = x^2 - x + 1 \), we substitute this into \( g(x) = 2 - x \):
\[
g(h(x)) = 2 - (x^2 - x + 1) = 2 - x^2 + x - 1 = 1 - x^2 + x.
\]
Thus, \( g \circ h(x) = 1 - x^2 + x \).

### Step 2: Find \( f \circ (g \circ h)(x) \)
Now, we apply \( f \) to the result of \( g \circ h(x) \). That is, \( f(g \circ h(x)) = f(1 - x^2 + x) \).

Substitute \( 1 - x^2 + x \) into \( f(x) = x + 4 \):
\[
f(1 - x^2 + x) = (1 - x^2 + x) + 4 = -x^2 + x + 1 + 4 = -x^2 + x + 5.
\]

Thus, \( f \circ (g \circ h)(x) = -x^2 + x + 5 \).

### Final Answer:
\[
f \circ (g \circ h)(x) = -x^2 + x + 5.
\]

Would you like further details or clarifications?

Here are 5 related questions to explore:
1. What is the difference between composing two functions and multiplying them?
2. How do you find the inverse of a composite function?
3. Can you explain the domain and range of \( f \circ g(x) \)?
4. How does composition affect the order of operations in functions?
5. How would the result change if \( f(x) = x^2 + 4 \) instead?

**Tip:** When composing functions, always apply the innermost function first, then move outward.

diket=f(x)=x+4  g(x)=2-x  h(x)=x²-x+1. tentukan fungsi (fo(goh)(x)?

Find the composition of functions f(g(h(x))) where f(x) = x + 4, g(x) = 2 - x, and h(x) = x² - x + 1. This problem involves function composition and quadratic functions, providing a detailed step-by-step solution suitable for Grades 9-12.

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