Pert 4-fungsi-operasi-dan-sifat (1)
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Transcript of Pert 4-fungsi-operasi-dan-sifat (1)
![Page 1: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/1.jpg)
FUNGSI (LANJUTAN)
OLEH;
DEDEH HODIYAH
![Page 2: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/2.jpg)
OPERASI FUNGSI
Fungsi f dan g dapat dioperasikan untuk
mendapatka fungsi baru
1. (f + g)(x) = f(x) + g(x)
2. (f – g)(x) = f(x) – g(x)
3. (f.g)(x) = f(x).g(x)
4. (f/g)(x) = f(x)/g(x)
![Page 3: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/3.jpg)
Contoh :
Diketahui f(x) = 2x + 3 , dan g(x) = x –
1
Maka :
1. (f+g)(x) = f(x) + g(x)
= (2x + 3) + (x – 1)
= 3x + 2
2. (f-g)(x) = f(x) – g(x)
= (2x + 3) – (x – 1)
= x + 4
![Page 4: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/4.jpg)
Diketahui f(x) = 2x + 3 , dan g(x) = x – 1
3. (f. g)(x) = f(x).g(x)
= (2x + 3)(x – 1)
=
4. (f/g)(x) = f(x)/g(x)
= (2x – 3)/(x – 1)
![Page 5: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/5.jpg)
Contoh 2 :
Diketahui :
Tentukan :
a. (f + g)(x)
b. (f – g)(x)
c. (f.g)(x)
d. (f/g) (x)
![Page 6: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/6.jpg)
Selain keempat operasi tersebut bisa
juga suatu fungsi dipangkatkan
Contoh :
1. Jika
dengan daerah asal [-1, ∞) dan [-
3,3)
Tentukan :
(f+g)(x) , (f-g)(x) , (f.g)(x) dan (f/g)(x)
![Page 7: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/7.jpg)
KOMPOSISI FUNGSI
PERHATIKAN GAMBAR BERIKUT
A B C
X Y Z
f g
h = (g o f) = g(f(x))
![Page 8: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/8.jpg)
Contoh :
1. Diketahui f(x) = 3x – 2 , dan g(x) = x
+ 5
Tentukan :
a. (f o g)(x)
b. (g o f)(x)
c. (f o g) (3)
d. (g o f)(-2)
![Page 9: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/9.jpg)
Contoh 2 :
Tentukan (f o g)(x) dan (g o f)(x) dari
fungsi-fungsi berikut :
1.
2.
![Page 10: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/10.jpg)
Contoh 3 :
Diketahui fungsi f(x) = x + 3 dan
(f o g)(x) = x2 + 6x + 7
Tentukan :
f(x) dan f(2)
Contoh 4 :
Diketahui g(x) = x2 - 3x + 1
Dan (f o g)(x) = 2x2 - 6x – 1
Tentukan f(x)
![Page 11: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/11.jpg)
FUNGSI INVERS
Suatu fungsi f : A → B mempunyai fungsi invers f-1 : B →A , jika semua elemen
himpunan A dan elemen himpunan B
berkorespondensi satu-satu
![Page 12: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/12.jpg)
Perhatikan gambar berikut !
Fungsi invers
A B
YX
f
f-1
![Page 13: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/13.jpg)
Contoh :
Tentukan invers dari fungsi berikut :
1. Diketahui f(x) = 3x – 5
Jawab :
Misal y = f(x)
y= 3x – 5
3x = y + 5
![Page 14: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/14.jpg)
Contoh :
Diketahui
Tentukan
Jawab :
![Page 15: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/15.jpg)
Cara cepat :
Jika
Maka
![Page 16: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/16.jpg)
FUNGSI INVERS DARI FUNGSI
KOMPOSISI
![Page 17: Pert 4-fungsi-operasi-dan-sifat (1)](https://reader031.fdocument.pub/reader031/viewer/2022013120/5a65b0517f8b9aa4758b5bd1/html5/thumbnails/17.jpg)
SEKIAN
TERIMA KASIH