Math Problem Statement

buatkan representasi graf

buatkan representasi graf

Solution

I have displayed the image you uploaded. Based on its content, it shows two mathematical functions from examples (Contoh 45 and Contoh 46). I will now create graph representations for the two functions mentioned.

For Contoh 45, the functions appear to be:

  • g={(1,w),(2,u),(3,v)}g = \{ (1, w), (2, u), (3, v) \}
  • f={(u,y),(v,z),(w,z)}f = \{ (u, y), (v, z), (w, z) \}
  • The composition fgf \circ g is {(1,y),(2,y),(3,z)}\{ (1, y), (2, y), (3, z) \}

For Contoh 46, the functions are:

  • f(x)=x1f(x) = x - 1
  • g(x)=x2+1g(x) = x^2 + 1
  • You are asked to find fg(x)f \circ g(x) and gf(x)g \circ f(x).

I'll generate graphs for these functions now.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you have any other questions or would like further explanations, feel free to ask!

Here are five questions related to the content:

  1. What does the composition of functions fgf \circ g represent in terms of mappings?
  2. How can you calculate the inverse of a function composition?
  3. What are the domain and range of the function f(x)=x1f(x) = x - 1?
  4. How does the behavior of g(x)=x2+1g(x) = x^2 + 1 differ from other quadratic functions?
  5. What are some applications of function composition in real-world problems?

Tip: Always remember that the order of composition of functions matters, f(g(x))f(g(x)) is different from g(f(x))g(f(x)).

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Math Problem Analysis

Mathematical Concepts

Function Composition
Mapping
Quadratic Functions

Formulas

f(x) = x - 1
g(x) = x^2 + 1
Composition of functions: f(g(x)) and g(f(x))

Theorems

Function Composition
Quadratic Function Behavior

Suitable Grade Level

Grades 10-12