Contoh Soal Fungsi Komposisi dan Fungsi Invers
1. Contoh soal Fungsi Komposisi
1. Misalkan f ={(1, 4), (2, 3), (3, 1), (4, 2)} dan g = {(1, 2), (2, 4), (3, 1), (4, 3)}, maka tentukanlah :
a. f o g
b. g o f
Jawab :
a. f o g = f [ g ]
= f [ (1, 2), (2, 4), (3, 1), (4, 3) ]
= {(1, 2)→(2, 3), (2, 4)→(4, 2), (3, 1)→(1, 4), (4, 3)→(3, 1)}
= {(1, 3), (2, 2), (3, 4), (4, 1)}
b. g o f = g [ f ]
= g [(1, 4), (2, 3), (3, 1), (4, 2) ]
= {(1, 4)→(4, 3), (2, 3)→(3, 1), (3, 1)→(1, 2), (4, 2)→(2, 4)}
= {(1, 3), (2, 1), (3, 2), (4, 4)}
2. Diberikan dua buah fungsi yang masing-masing f (x) dan g (x) berturut-turut yaitu :
f (x) = 5x + 4
g (x) = 7 – x
Tentukanlah:
a. (f o g) (x)
b. (g o f) (x)
Jawab :
a. (f o g)(x) = f (g(x)) = f (7 – x) = 5 (7 – x) + 4 = 35 – 5x + 4 = 39 – 5x
b. (g o f)(x) = g(f(x)) = g (5x + 4) = 7 – (5x + 4) = 7 – 4 – 5x = 3 – 5x
3. Diketahui dua fungsi f(x)=x2−5x+4 dan \(g(x)= x^{2}+3x-6\). Tentukanlah nilai (f o g)(2)
Jawab :
(f o g)(2) = f [ g(2) ]
=f [(2)2+3(2)−6]
= f [4 + 6 – 6]
= f [4]
= 42– 5(4) + 4
= 16 – 20 + 4
= 0
4. Diketahui f(x – 2) = x2+5x–3 maka tentukanlah f(x)!
Jawab :
f(x – 2) = x2+5x–3
Misalkan x – 2 = m maka x = m + 2
sehingga f(m) = (m+2)2 + 5(m + 2)– 3
f(m) = m2+ 4m + 4 + 5m + 10 – 3
f(m) =m2+ 9m + 11
Jadi f(x) = x2+ 9x + 11
2. Contoh Soal Fungsi Invers
Jawab :
Misalkan y = x²– 7x + 12 maka mencari nilai f−¹ (2) dapat dilakukan dengan mensubstitusikan nilai y = 2, sehingga
Komentar
Posting Komentar