Question

Jika 2 f(x) = 3x + f (1/x), maka f(3) adalah
A. 19/3
B. 3/19
C. 17/5
D. 5/17

Beserta cara yaa, makasih

Answer 1

2 f(x) = 3x + f (1/x)

2 f(3) = 3(3) + f(1/3) --> 2 f(3) = 9 + f(1/3)
2 f(3) - f(1/3) =  9

2 f(1/3) =3(1/3) + f(3)-->2 f(1/3) = 1 + f(3)
f(3) - 2 f(1/3) = -1

2. f(3) - f(1/3) = 9 ......kalikan 2
f(3) - 2 f(1/3) = -1 ......kalikan 1

4 f(3) - 2 f(1/3) = 18
f(3) - 2 f(1/3) = -1
kurangkan
3 f(3) = 19
f(3) = 19/3

Answer 2

2f(x) = 3x + f(1/x)

Ambil x = 3
2f(3) = 3(3) + f(1/3) ⇒ 2f(3) - f(1/3) = 9

Ambil x = 1/3
2f(1/3) = 3(1/3) + f(1/(1/3)) ⇒ f(3) - 2f(1/3) = -1

Berdasarkan persamaan" yang sudah didapat

2f(3) - f(1/3) = 9 |x2| ⇒ 4f(3) - 2f(1/3) = 18
f(3) - 2f(1/3) = -1|x1| ⇒   f(3) - 2f(1/3) = -1  -
                                                   3f(3) = 19
                                                 ⇒ f(3) = 19/3

Jawab : A


Terimakasih smoga membantu