Diketahui f(x)=x²+3x-5, g(x)=4x-1, h(x) 3x+2 tentukan fog(x)

Untuk menentukan \( f \circ g(x) \) (atau \( f(g(x)) \)), kita perlu mengganti setiap \( x \) dalam fungsi \( f(x) \) dengan \( g(x) \).

Diketahui: 
\[ f(x) = x^2 + 3x - 5 \]
\[ g(x) = 4x - 1 \]

Kita ingin mencari \( f(g(x)) \):
1. Substitusi \( g(x) = 4x - 1 \) ke dalam \( f(x) \):
\[ f(g(x)) = f(4x - 1) \]

2. Hitung \( f(4x - 1) \) dengan memasukkan \( 4x - 1 \) ke dalam \( f(x) = x^2 + 3x - 5 \):
\[ f(4x - 1) = (4x - 1)^2 + 3(4x - 1) - 5 \]

3. Selesaikan step-by-step:
   - Hitung \( (4x - 1)^2 \):
     \[
     (4x - 1)^2 = (4x)^2 - 2 \times 4x \times 1 + 1^2 = 16x^2 - 8x + 1
     \]
   - Hitung \( 3(4x - 1) \):
     \[
     3(4x - 1) = 12x - 3
     \]

4. Masukkan hasil di atas ke dalam persamaan:
\[ 
f(4x - 1) = 16x^2 - 8x + 1 + 12x - 3 - 5
\]

5. Sederhanakan:
\[ 
f(4x - 1) = 16x^2 + 4x - 7
\]

Jadi, \( f \circ g(x) = f(g(x)) = 16x^2 + 4x - 7 \).

Diketahui f(x)=x²+3x-5, g(x)=4x-1, h(x)=3x+2 tentukan fog(x)

Learn how to find the composition of two functions, f(x) = x² + 3x - 5 and g(x) = 4x - 1. This detailed solution involves substituting one function into another, expanding and simplifying quadratic expressions, and is ideal for students in Grades 9-10.

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