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

MAPEL : MATEMATIKA

KELAS : X

BAB : FUNGSI KOMPOSISI
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Diketahui :
↪f(x) = 2x + 5
↪g(x) = (x - 1)/(x + 4)
↪(f o g) (a) = 5

Ditanya :
↪Nilai a


Jawaban :
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➡Tentukan fungsi (f o g) (x)

(f o g) (x) = f(g(x)) = f(x - 1/ x + 4)

(f o g) (x) = 2(x - 1/ x + 4) + 5

(f o g) (x) = (2x - 2/x + 4) + 5

(f o g) (x) = (2x - 2)/(x + 4) + (5x + 20)/(x + 4)

(f o g) (x) = (7x + 18)/(x + 4)


Sehingga, nilai a adalah

f(a) = 5

(7x + 18)/(x + 4) = 5

7x + 18 = 5(x + 4)

7x + 18 = 5x + 20

7x - 5x = 20 - 18

2x = 2

x = 2/2

x = 1



Sehingga, nilai a = 1 ✔



Semoga membantu.. :)