Jika f(x) = 2x + 5 dan g(x) = x-1/ x+4, x≠-4, maka (fog)(x) =.

Diberikan dua fungsi:
- \( f(x) = 2x + 5 \)
- \( g(x) = \frac{x - 1}{x + 4} \), dengan syarat \( x \neq -4 \)

Kita diminta mencari komposisi \( (f \circ g)(x) \), yang artinya \( f(g(x)) \). Ini berarti kita akan mengganti \( g(x) \) ke dalam fungsi \( f(x) \).

### Langkah-langkah:

1. **Substitusi \( g(x) \) ke dalam fungsi \( f(x) \):**

\[
f(g(x)) = f\left(\frac{x - 1}{x + 4}\right)
\]

Fungsi \( f(x) = 2x + 5 \), sehingga:

\[
f\left(\frac{x - 1}{x + 4}\right) = 2\left(\frac{x - 1}{x + 4}\right) + 5
\]

2. **Sederhanakan ekspresi:**

\[
= \frac{2(x - 1)}{x + 4} + 5
\]

\[
= \frac{2x - 2}{x + 4} + 5
\]

3. **Gabungkan pecahan:**

Ubah 5 menjadi pecahan dengan penyebut \( x + 4 \):

\[
= \frac{2x - 2}{x + 4} + \frac{5(x + 4)}{x + 4}
\]

\[
= \frac{2x - 2 + 5(x + 4)}{x + 4}
\]

4. **Selesaikan:**

\[
= \frac{2x - 2 + 5x + 20}{x + 4}
\]

\[
= \frac{7x + 18}{x + 4}
\]

### Kesimpulan:
\[
(f \circ g)(x) = \frac{7x + 18}{x + 4}, \quad x \neq -4
\]

Apakah ada hal lain

Jika f(x) = 2x + 5 dan g(x) = x - 1 / x + 4, x ≠ -4, maka (fog)(x) =

Learn how to compose functions f(x) = 2x + 5 and g(x) = (x - 1)/(x + 4) to find (fog)(x). This problem explores function composition, algebraic manipulation, and rational functions. Step-by-step solution for Grades 9-11.

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