Math Problem Statement

Diketahui f(x) = 3 - 2x, g(x) = x + 4, dan h(x) = 2x + 1. Tentukan (f ∘ g ∘ h)(x)!

Solution

The image shows a mathematical question written in Indonesian. Here's the problem in the image:


Diketahui:
f(x)=32xf(x) = 3 - 2x,
g(x)=x+4g(x) = x + 4,
h(x)=2x+1h(x) = 2x + 1.
Tentukan (fgh)(x)(f \circ g \circ h)(x)!


This question is asking for the composition of functions, specifically (fgh)(x)(f \circ g \circ h)(x), which means f(g(h(x)))f(g(h(x))).

Step-by-Step Solution:

  1. Find h(x)h(x): h(x)=2x+1h(x) = 2x + 1

  2. Substitute h(x)h(x) into g(x)g(x): g(h(x))=g(2x+1)=(2x+1)+4=2x+5g(h(x)) = g(2x + 1) = (2x + 1) + 4 = 2x + 5

  3. Substitute g(h(x))g(h(x)) into f(x)f(x): f(g(h(x)))=f(2x+5)=32(2x+5)=3(4x+10)=34x10=4x7f(g(h(x))) = f(2x + 5) = 3 - 2(2x + 5) = 3 - (4x + 10) = 3 - 4x - 10 = -4x - 7

Thus, the composition of the functions is: (fgh)(x)=4x7(f \circ g \circ h)(x) = -4x - 7

Would you like further details or have any other questions?

5 Related Questions:

  1. What is the meaning of function composition?
  2. How would the result change if f(x)f(x), g(x)g(x), or h(x)h(x) were different functions?
  3. Can you explain the importance of the order in which functions are composed?
  4. How do you differentiate a composition of functions?
  5. What happens if you reverse the order of composition, such as (hgf)(x)(h \circ g \circ f)(x)?

Tip:

Always evaluate the innermost function first when solving compositions, as the order of operations in function composition is critical for accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Composition

Formulas

f(g(h(x)))
Substitute functions sequentially

Theorems

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Suitable Grade Level

Grades 9-12