Diketahui (gof)(x)=4x+7/x+5 ,dan g(x)=3x-5,rumus fungsi dari g(x) adalah

Diketahui (gof)(x)=4x+7/x+5 ,dan g(x)=3x-5,rumus fungsi dari g(x) adalah

Jawaban: f(x) = (3x-6)/(x+5)

Konsep: Fungsi Komposisi
Fungsi komposisi merupakan penggabungan operasi dua jenis fungsi f(x) dan g(x) sehingga menghasilkan sebuah fungsi baru. Operasi fungsi komposisi biasa dilambangkan dengan “o” dan dibaca komposisi atau bundaran. Fungsi baru yang dapat terbentuk dari f(x) dan g(x) adalah:
1. (f o g)(x) artinya g dimasukkan ke f
2. (g o f)(x) artinya f dimasukkan ke g

Asumsi soal:
Diketahui (gof)(x)=4x+7/x+5 ,dan g(x)=3x-5,rumus fungsi dari f(x) adalah

Pembahasan:
(g o f)(x) = g(f(x))
4x+7/x+5 = 3(f(x)) – 5 ….. (1)
4x+7 = (3(f(x))-5)(x+5)
4x+7 = 3x(f(x))+15(f(x))- 5x+25
4x+7+5x-25 = 3x(f(x))+15(f(x))
9x-18 = 3x(f(x))+15(f(x))
3x-6 = x(f(x))+5(f(x))
3x-6 = f(x) (x+5)
f(x) = (3x-6)/(x+5)

Jadi, rumus fungsi f(x) adalah f(x) = (3x-6)/(x+5).

Baca Juga :  Complete the sentences with a form of the verb in parentheses. Three hundred and fifty years ago, people (1. make) /made/ their own clothes. They (2. have, not) _____ machines for making clothes. There (3. be, not) _____ any clothing factories. People (4. tear) _____ homemade clothes that were sewn by hand. Today, very few people (5. make) _____ their own clothes. Clothing (6. come) _____ ready-made from factories. People (7. buy) _____ almost all their clothes from stores. The modern clothing industry (8. be) _____ international. As a result, people from different countries often (9. wear) _____ similar clothes. For example, people in many different countries throughout the world (10. wear) _____ jeans and t-shirts. However, some regional differences in clothing still (11. exist) _____ for instance, people of the Arabian deserts (12. wear) _____ loose, flowing lobes to protect themselves from the heat of the sun. In parts of Northern Europe, fur hats (13. be) _____ common in the winter. In the future, there (14. be, probably) _____ fewer and fewer differences in clothing. People throughout the world (15. wear) _____ clothes from the same factories. (16. We all, dress) _____ in the future? TV shows and movies about the future often (17. show) _____ everybody in a uniform of some kind. What (18. you, think) _____? Number 18