Question

Tolong jawab nomor 7,9,10 saja pakai cara. Terima kasih.

Answer 1

Verified answer

Jawab
7. 
gof(x) =  g {f(x)}
gof(x) =  g { (x-1)/(x)}
gof(x) =  (x - 1)/x  + 3
y = (x -1)/x + 3
(x - 1)/x = y - 3
x - 1 = x(y - 3)
x - 1 = xy - 3x
x + 3x - xy  = 1
2x - xy = 1
x(2 - y) =1
x = 1/ (2 - y)
(gof)⁻¹(x)= 1/ (2 - x)

9.
fog(x+1) = -2x^2 - 4x - 1
fog(x) = -2(x -1)^2 - 4(x -1) - 1
fog(x)= -2(x^2 - 2x + 1) - 4x + 4- 1
fog(x) = - 2x^2 + 4x - 2 - 4x  + 3
fog(x) = -2x^2 +1
f {g(x)} = -2 x^2 + 1
2. g(x)  + 3 = -2x^2 + 1
2. g(x) = - 2x^2 - 2
g(x) = - x^2 - 1

y = -x^2 - 1
x^2 = - y - 1
x = √(-y -1)
g⁻¹(x)= √(-x - 1)

g⁻¹(-2)= √(2-1) = 1

10
f(x) = x + 2 
g(x)= 2x

fog(x)= .f{ g(x)} = f (2x)
fog(x) = 2x+ 2
y = 2x + 2
2x = y -2
x = 1/2 y - 1
(fog)⁻¹(x) = 1/2 x - 1

gof(x) = g{ f(x)} = g (x+ 2)
gof(x) = 2(x +2) 
y = 2(x+2)
x + 2 = 1/2 y
x = 1/2 y - 2
(gof)⁻¹(x)= 1/2 x - 2