Math Problem Statement
Jika f(x) = 2x + 5 dan g(x) = x-1/ x+4, x≠-4, maka (fog)(x) =.
Solution
Diberikan dua fungsi:
- , dengan syarat
Kita diminta mencari komposisi , yang artinya . Ini berarti kita akan mengganti ke dalam fungsi .
Langkah-langkah:
- Substitusi ke dalam fungsi :
Fungsi , sehingga:
- Sederhanakan ekspresi:
- Gabungkan pecahan:
Ubah 5 menjadi pecahan dengan penyebut :
- Selesaikan:
Kesimpulan:
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Math Problem Analysis
Mathematical Concepts
Function Composition
Algebra
Rational Functions
Formulas
f(g(x)) = f(g(x)) = 2(g(x)) + 5
g(x) = (x - 1) / (x + 4)
Theorems
Function Composition
Suitable Grade Level
Grades 9-11
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