Dik: fungsi f(x) = 5x +3 dan g(x)=x²+²×Tentukanlah
A. (fog)(x)
B. (gof)(x)
C. (fog) (-1)
D. (gof) (2)![]()
A. (fog)(x)
B. (gof)(x)
C. (fog) (-1)
D. (gof) (2)
Jawaban:
- Maka hasil dari (fog)(x) adalah 5x² + 10x + 3
- Maka hasil dari (gof)(x) adalah 25x² + 40x + 15
- Maka hasil dari (fog)(-1) adalah -2
- Maka hasil dari (gof)(2) adalah 195
Penjelasan dengan langkah-langkah:
Diketahui :
- f(x) = 5x + 3
- g(x) = x² + 2x
Ditanya :
- (fog)(x)
- (fog)(x) (gof)(x)
- (fog)(x) (gof)(x) (fog)(-1)
- (fog)(x) (gof)(x) (fog)(-1) (gof) (2)
Jawaban :
Mencari (fog)(x)
- (fog)(x) = f{g(x)}
- (fog)(x) = f(x² + 2x)
- (fog)(x) = 5(x² + 2x) + 3
- (fog)(x) = 5x² + 10x + 3
Mencari (gof)(x)
- (gof)(x) = g{f(x)}
- (gof)(x) = g(5x + 3)
- (gof)(x) = (5x + 3)² + 2(5x + 3)
- (gof)(x) = (25x² + 30x + 9) + 10x + 6
- (gof)(x) = 25x² + 30x + 9 + 10x + 6
- (gof)(x) = 25x² + 40x + 15
Mencari (fog)(-1)
- (fog)(x) = 5x² + 10x + 3
- (fog)(-1) = 5(-1)² + 10(-1) + 3
- (fog)(-1) = 5(1) + (-10) + 3
- (fog)(-1) = 5 + (-10) + 3
- (fog)(-1) = -5 + 3
- (fog)(-1) = -2
Mencari (gof)(2)
- (gof)(x) = 25x² + 40x + 15
- (gof)(2) = 25(2)² + 40(2) + 15
- (gof)(2) = 25(4) + 80 + 15
- (gof)(2) = 100 + 80 + 15
- (gof)(2) = 180 + 15
- (gof)(2) = 195
Diketahui:
- f(x) = 5x + 3
- g(x) = x² + 2x
Ditanyakan:
- A. (fog)(x)
- B. (gof)(x)
- C. (fog)(-1)
- D. (gof)(2)
Jawab:
Bagian (A)
(fog)(x) = f(g(x))
(fog)(x) = f(x² + 2x)
(fog)(x) = 5(x² + 2x) + 3
(fog)(x) = 5x² + 10x + 3
Bagian (B)
(gof)(x) = g(f(x))
(gof)(x) = g(5x + 3)
(gof)(x) = (5x + 3)² + 2x
(gof)(x) = 5x(5x + 3) + 3(5x + 3) + 2(5x + 3)
(gof)(x) = 25x² + 15x + 15x + 9 + 10x + 6
(gof)(x) = 25x² + 40x + 25
Bagian (C)
(fog)(x) = 5x² + 10x + 3
(fog)(-1) = 5(-1)² + 10(-1) + 3
(fog)(-1) = 5 - 10 + 3
(fog)(-1) = -5 + 3
(fog)(-1) = -2
Bagian (D)
(gof)(x) = 25x² + 32x + 9
(gof)(2) = 25(2)² + 32(2) + 9
(gof)(2) = 25(4) + 64 + 9
(gof)(2) = 100 + 64 + 9
(gof)(2) = 164 + 9
(gof)(2) = 173
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