Respuesta :
Answer:
The domain is [tex]{(-2,1),(-1,2),(-3,\dfrac{5}{3})}[/tex]
Step-by-step explanation:
Given that,
The function is
[tex]f(x,y)=(-2x,-3y+1)[/tex]
The coordinates of range are,
[tex]range=(4,-2), (2,-5), (-6,4)}[/tex]
The domain is,
[tex]Domain={(x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3})}[/tex]
We need to find the value of x₁ and y₁
Using given function
[tex]f(x.y)=(-2x,-3y+1)[/tex]
[tex]f(x_{1},y_{1})=(4,-2,)[/tex]
[tex](-2x_{1},-3y_{1}+1)=(4,-2)[/tex]
On equating value of x
[tex]-2x_{1}=4[/tex]
[tex]x_{1}=-2[/tex]
On equating value of y
[tex]-3y_{1}+1=-2[/tex]
[tex]-3y_{1}=-2-1[/tex]
[tex]y_{1}=\dfrac{-2-1}{-3}[/tex]
[tex]y_{1}=1[/tex]
We need to find the value of x₂ and y₂
Using given function
[tex]f(x_{2},y_{2})=(2,-5,)[/tex]
[tex](-2x_{2},-3y_{2}+1)=(2,-5)[/tex]
On equating value of x
[tex]-2x_{2}=2[/tex]
[tex]x_{2}=-1[/tex]
On equating value of y
[tex]-3y_{2}+1=-5[/tex]
[tex]-3y_{2}=-5-1[/tex]
[tex]y_{2}=\dfrac{-5-1}{-3}[/tex]
[tex]y_{2}=2[/tex]
We need to find the value of x₃ and y₃
Using given function
[tex]f(x_{3},y_{3})=(-6,4,)[/tex]
[tex](-2x_{3},-3y_{3}+1)=(-6,4)[/tex]
On equating value of x
[tex]-2x_{3}=-6[/tex]
[tex]x_{3}=-3[/tex]
On equating value of y
[tex]-3y_{3}+1=-4[/tex]
[tex]-3y_{3}=-4-1[/tex]
[tex]y_{3}=\dfrac{-4-1}{-3}[/tex]
[tex]y_{3}=\dfrac{5}{3}[/tex]
We need to find the domain
Using domain
[tex]Domain={(-2,1),(-1,2),(-3,\dfrac{5}{3})}[/tex]
Hence, The domain is [tex]{(-2,1),(-1,2),(-3,\dfrac{5}{3})}[/tex]
