Question

100 POINT

1)
jika f(x) = 2x +1
g(x) = 5x-2. Maka f°g -¹ (x) adalah?

2)Tentukan invers
jika f(x) = 2x²+5x-3 .

3)
Tentukan Invers .
f(x) = ² log (3x-4) .

4)
tentukan invers .
f(x) = 3^²x-¹

Answer 1

Verified answer

Bab Fungsi Komposisi
Matematika SMA Kelas X

nomor 1
(fog) (x) = f(5x - 2)
(fog) (x) = 2 (5x - 2) + 1
(fog) (x) = 10x - 4 + 1
(fog) (x) = 10x - 3
y = 10x - 3
10x = y + 3
x = (y + 3)/10
f⁻¹ (x) = (x + 3)/10

nomor 2
f(x) = 2x² + 5x - 3
y = 2x² + 5x - 3
(2x² + 5x - 3)/2 = y/2
x² + 5x/2 - 3/2 = y/2
(x + 5/4)² - 31/4 = y/2
(x + 5/4)² = 31/4 + y/2
(x + 5/4)² = 31/4 + 2y/4
x + 5/4 = √((2y + 31)/4)
x = -5/4 + 1/2 √(2y + 31)
f⁻¹ (x) = -5/4 + (1/2) √(2x + 31)

nomor 3
f(x) = ²log (3x - 4)
y = ²log (3x - 4)
3x - 4 = 2^y
3x = 4 + 2^y
x = (4 + 2^y)/3
f^-1 (x) = (4 + 2^x)/3

nomor 4
f(x) = 3²ˣ⁻¹
y = 3²ˣ⁻¹
³log y = 2x - 1
2x - 1 = ³log y
2x = 1 + ³log y
x = (1 + ³log y)/2
f⁻¹ (x) = (1 + ³log x)/2