Olimpiade Sains Kota (OSK) 2015 - Matematika SMA, Nomor 3

Question

Jika (f o g)(x) = \frac{7x+3}{5x-9} dan g(x) = 2x – 4, maka nilai f(2) adalah ....

Bocah Bodoh · Accepted Answer

Nih jawaban cepet. (fog)(x)=(7x+3)/(5x-9)
f(g(x))=(7x+3)/(5x-9) ini memiliki arti variabel x milik fungsi g(x) . maka yg diminta f(2) maka g(x) harus sama dengan 2.

-> g(x)=2 -> 2x - 4 = 2 -> x=3 . ketemu nilai x sub. ke (fog)(x) . f(g(x))=(7x+3)/(5x-9) -> f(2)=(7.3+3)/(5.3-9)=24/6=4.

Ali Jaya Meilio · Answer

(f o g)(x) = (7x + 3) / (5x - 9)

f(g(x)) = (7g(x) + 3) / (5g(x) - 9) ... (1)

g(x) = 2x - 4 ... (2)

Subt. (2) ke (1)

f(2x - 4) = (7(2x-4) + 3) / (5(2x-4) - 9)

f(2x - 4) = (14x - 28 + 3) / (10x - 20 - 9)

f(2x - 4) = (14x - 25) / (10x - 29) ... (3)

Misalkan y = 2x - 4 ... (4)

2x = y + 4

x = y/2 + 2 ... (5)

Subt. (4) dan (5) ke (3)

f(y) = (14(y/2 + 2) - 25) / (10(y/2 + 2) - 29)

f(y) = (7y + 28 - 25) / (5y + 20 - 29)

f(y) = (7y + 3) / (5y - 9) ... (6)

f(2) = (7*2 + 3) / (5*2 - 9)

= (14 + 3) / (10 - 9)

= 17 / 1

= 17

tiara anggraini gaib · Answer

????(2???? 4) = 7???? + 3 5???? 9 Misalkan ???? = 2???? 4 maka ???? = ????+4 2 . ????(????) = 7 ? ???? + 4 2 ? + 3 5 ? ???? + 4 2 ? 9 = 7???? + 34 5???? + 2 Yang setara dengan ????(????) = 7???? + 34 5???? + 2 ????(2) = 7(2) + 34 5(2) + 2 = 4 Jadi, nilai f(2) adalah 4.

sutarmin jundan · Answer

f(g(x)) = (7x+3)/(5x-9)

f(2x-4)= (7x+3)/(5x-9)

misal, a = 2x - 4 maka x = (a + 4)/2

maka

f(a) = (7((a + 4)/2) + 3)/(5((a + 4)/2)-9)

f(a) = (7a + 34)/(5a + 2)

f(2) = (7(2) + 34)/(5(2) + 2)

f(2) = 48/12 = 4

tapi terlalu panjang pake aja g(x) = 2 lebih mudah. ini hanya alternatif lain.

f3rzpq12 f3rzpq12 · Answer

XXX.COM

Abdul Hadi · Answer

4

Olimpiade Sains Kota (OSK) 2015 - Matematika SMA, Nomor 3

6 jawaban