diketahui (f°g) (x)= x²+4x+3dan f(x)=x²-1 tentukan nilai (g°f)(3)

Halo Yenita. Terima kasih sudah bertanya di Roboguru. Jawaban : (gof)(3) = ±10 Perhatikan penjelasan berikut ya. Ingat kembali pada komposisi fungsi f(x) dan g(x) berlaku: (fog)(x) = f(g(x)) (gof)(x) = g(f(x)) Diketahui: (fog)(x) = x² + 4x + 3 dan f(x) = x² - 1 Ditanya : (gof)(3) = ... ? Maka: (fog)(x) = x² + 4x + 3 f(g(x)) = x² + 4x + 3 (g(x))² - 1 = x² + 4x + 3 (g(x))² = x² + 4x + 3 + 1 (g(x))² = x² + 4x + 4 g(x) = ±√(x² + 4x + 4) Sehingga: (gof)(x) = g(f(x)) (gof)(x) = g(x² - 1) (gof)(x) = ±√((x²-1)² + 4(x²-1) + 4) (gof)(3) = ±√((3²-1)² + 4(3²-1) + 4) (gof)(3) = ±√((9-1)² + 4(9-1) + 4) (gof)(3) = ±√(64 + 32 + 4) (gof)(3) = ±√100 (gof)(3) = ±10 Jadi, (gof)(3) = ±10. Semoga membantu.