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

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 dua persamaan yang 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


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