f(×)=2×+3,g(×)=×²-4,h(×)=×-2,i(×) tentukan (f°g°h°)(×-1)

To determine \((f \circ g \circ h)(x - 1)\), we need to work through the composition step-by-step. We are given the following functions:

\[
f(x) = 2x + 3,\quad g(x) = x^2 - 4,\quad h(x) = x - 2
\]

### Step-by-Step Solution:

1. **Start with \( h(x) \)**:  
   Since we are finding \((f \circ g \circ h)(x - 1)\), let's first evaluate \( h(x - 1) \).  
   \[
   h(x - 1) = (x - 1) - 2 = x - 3
   \]

2. **Next, apply \( g(x) \) to \( h(x - 1) \)**:  
   Now, substitute \( h(x - 1) = x - 3 \) into \( g(x) \).  
   \[
   g(h(x - 1)) = g(x - 3) = (x - 3)^2 - 4 = x^2 - 6x + 9 - 4 = x^2 - 6x + 5
   \]

3. **Finally, apply \( f(x) \) to \( g(h(x - 1)) \)**:  
   Now substitute \( g(h(x - 1)) = x^2 - 6x + 5 \) into \( f(x) \).  
   \[
   f(g(h(x - 1))) = f(x^2 - 6x + 5) = 2(x^2 - 6x + 5) + 3
   \]
   Simplifying this expression:
   \[
   f(g(h(x - 1))) = 2x^2 - 12x + 10 + 3 = 2x^2 - 12x + 13
   \]

Thus, the result is:
\[
(f \circ g \circ h)(x - 1) = 2x^2 - 12x + 13
\]

### Do you want further details or have any questions?

Here are some related questions to expand your understanding:
1. What is \((f \circ h)(x)\) for the same functions?
2. How do we compute \((g \circ f)(x)\)?
3. What would be the derivative of \( f(g(h(x))) \)?
4. Can you find \((f \circ g \circ h)(2)\)?
5. How would the result change if \( h(x) \) was instead \( x + 2 \)?

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

f(x) = 2x + 3, g(x) = x² - 4, h(x) = x - 2, i(x): Tentukan (f°g°h)(x-1)

Learn how to solve the composite function (f ° g ° h)(x - 1) with detailed step-by-step instructions. The problem involves linear and quadratic functions and covers essential concepts of function composition. Suitable for students in Grades 9-12.

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