Question

1) Jika f(x)=2x-5/3x-2 maka f^-1(1)=..

2) f(x)=1/x. dan f(g(x))=x-3/2x maka g^-1(x)=...

Answer 1

1) y = (2x - 5)/(3x - 2)
3xy - 2y = 2x - 5
3xy - 2x = 2y - 5
x(3y - 2) = 2y - 5
x = (2y - 5)/(3y - 2)
f⁻¹(x) = (2x - 5)/(3x - 2)
f⁻¹(1) = -3

2) f(x) = 1/x
f(g(x)) = (x - 3)/2x
1/g(x) = (x - 3)/2x
g(x) (x - 3) = 2x
g(x) = 2x/(x - 3)
y = 2x/(x - 3)
xy - 3y = 2x
x(y - 2) = 3y
x = 3y/(y - 2)
g⁻¹(x) = 3x/(x - 2)