SOAL LATIHAN/TUGAS KALKULUS - PERTEMUAN 10
Nama : Tubagus Ardian Maulana
Kelas : 01TPLP015
NIM : 201011400661
SOAL
1. diketahui f(x) = √x dan g(x) = x+1, maka selesaikan:
a. f(x) ∘ g(x)
b. g(x) ∘ f(x)
c. f(x) ∘ f(x)
d. g(x) ∘ g(x)
2. Selesaikan Soal Berikut, f(x) = x^2 + 2x + 5 dan g(x) = 3x maka cari lah:
a. f(x) ∘ g(x)
b. g(x) ∘ f(x)
c. f(x) + g(x)
d. g(x) - f(x)
3. diketahui f(x) = x2 + 1 dan g(x) = 2x - 3, maka (f ∘ g)(x) =... diketahui fungsi f(x) = 3x - 1 dan g(x) = x^2 + 2x + 5, nilai dari komposisi fungsi (f ∘ g)(1) dan (g ∘ f)(2) adalah?
4. diberikan 2 buah fungsi:
f(x) = 2x - 3
g(x) = x2 + 2x + 3
jika (f ∘ g)(a) = 33, tentukan nilai dari 5a
JAWAB
1. a. (𝑓
∘
𝑔)(𝑥)
= (𝑓(𝑔(𝑥))
= √𝑥
+ 1
b. (𝑔
∘
𝑓)(𝑥)
= (𝑔(𝑓(𝑥))
= √𝑥
+ 1
c. (𝑓
∘
𝑓)(𝑥)
= (𝑓(𝑓(𝑥))
= √√𝑥
= 4√x
d. (𝑔
∘
𝑔)(𝑥)
= (𝑔(𝑔(𝑥))
= (𝑥
+ 1) + 1 = 𝑥
+ 2
2. a).
f(x) o g(x) = (f o g)(x) ==> (f(g(x)) = (3x)² + 2(3x) + 5
= 9x² + 6x + 5
b). g(x) o f(x) = (g o f)(x) ==> (g(f(x)) = 3(x² + 2x +
5)
= 3x² + 6x + 15
c). f(x) + g(x) ==> (x² + 2x + 5) + 3x
= x² + 5x + 5
d). g(x) - f(x) = 3x - (x² - 2x + 5)
= 3x -x²- 2x - 5
= -x² + x - 5
3. a.
f(x) = x2 +1
dan
g(x) = 2x - 3
(fog)(x) = f (g(x)) = (2x - 3)2 +
1 = 4x2 -
12x + 9 + 1 = 4x2 -
12x + 10
b. f(x) = 3x - 1 dan g(x) = x2 + 2x + 5
(fog)(1) = f(g(x)) = 3 (x2 + 2x + 5) + 1 = 3x2 + 6x + 15 + 1 = 3x2 + 6x + 16
(fog)(1) = 3 (1) + 6 (1) + 16 = 3 + 6 + 16 = 25
(gof)(2) = g(f(x)) = (3x - 1)2 + 2(3x - 1) + 5 = 9x - 6x + 1 + 6x - 2 + 5
(gof)(2) = 9x2 - 6x + 6x + 1 - 2 + 5 = 9x2 + 4 = 9(2)2 + 4 = 40
4. f(x)
= 2x - 3
g(x) = x² + 2x + 3
jika (f o g)(x) = 33, tentukan nilai 5a
Jawab :
f(a) o
g(a) = (f o g)(a) ==> (f(g(a)) = 2(x² + 2x + 3) - 3
33 = 2x² +
4x + 6 - 3
33 = 2x² +
4x + 3
33 - 3 =
2x² + 4x
30 = 2(3)²
+ 4(3)
30 = 18 +
12
30 = 30
= 30 -30
= 0
Nilai a =
3
5a = 5 x 3
= 15
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