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Tomtit [17]
3 years ago
11

If the range of the coordinate transformation f(x, y) = (-2x,-3y +1) is (4, -2), (2,-5),(-6,4), what

Mathematics
1 answer:
vazorg [7]3 years ago
6 0

Answer:

The domain is {(-2,1),(-1,2),(-3,\dfrac{5}{3})}

Step-by-step explanation:

Given that,

The function is

f(x,y)=(-2x,-3y+1)

The coordinates of range are,

range=(4,-2), (2,-5), (-6,4)}

The domain is,

Domain={(x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3})}

We need to find the value of x₁ and y₁

Using given function

f(x.y)=(-2x,-3y+1)

f(x_{1},y_{1})=(4,-2,)

(-2x_{1},-3y_{1}+1)=(4,-2)

On equating value of x

-2x_{1}=4

x_{1}=-2

On equating value of y

-3y_{1}+1=-2

-3y_{1}=-2-1

y_{1}=\dfrac{-2-1}{-3}

y_{1}=1

We need to find the value of x₂ and y₂

Using given function

f(x_{2},y_{2})=(2,-5,)

(-2x_{2},-3y_{2}+1)=(2,-5)

On equating value of x

-2x_{2}=2

x_{2}=-1

On equating value of y

-3y_{2}+1=-5

-3y_{2}=-5-1

y_{2}=\dfrac{-5-1}{-3}

y_{2}=2

We need to find the value of x₃ and y₃

Using given function

f(x_{3},y_{3})=(-6,4,)

(-2x_{3},-3y_{3}+1)=(-6,4)

On equating value of x

-2x_{3}=-6

x_{3}=-3

On equating value of y

-3y_{3}+1=-4

-3y_{3}=-4-1

y_{3}=\dfrac{-4-1}{-3}

y_{3}=\dfrac{5}{3}

We need to find the domain

Using domain

Domain={(-2,1),(-1,2),(-3,\dfrac{5}{3})}

Hence, The domain is {(-2,1),(-1,2),(-3,\dfrac{5}{3})}

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