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Step-by-step explanation:

Domain : {3, 4, 5, 6, 7}

Step-by-step explanation:

Given the function, f(x) = -2x + 13, and a range of {7, 5, 3, 1, -1}:

You can get the domain values algebraically by substituting the range values into the given function.  

f(x) = 7:

f(x) = -2x + 13

7 = -2x + 13

7 - 13 = -2x + 13 - 13

-6 = -2x

Divide both sides by -2 to solve for x:

-6/-2 = -2x/-2

3 = x

f(x) = 5:

f(x) = -2x + 13

5 = -2x + 13

5 - 13 = -2x + 13 - 13

-8 = -2x

Divide both sides by -2 to solve for x:

-8/-2 = -2x/-2

4 = x

f(x) = 3:

f(x) = -2x + 13

3 = -2x + 13

3 - 13 = -2x + 13 - 13

-10 = -2x

Divide both sides by -2 to solve for x:

-10/-2 = -2x/-2

5 = x

f(x) = 1:

f(x) = -2x + 13

1 = -2x + 13

1 - 13 = -2x + 13 - 13

-12 = -2x

Divide both sides by -2 to solve for x:

-12/-2 = -2x/-2

6 = x

f(x) = -1:

f(x) = -2x + 13

-1 = -2x + 13

-1 - 13 = -2x + 13 - 13

-14 = -2x

Divide both sides by -2 to solve for x:

-14/-2 = -2x/-2

7 = x

Therefore, the domain of the function, f(x) = -2x + 13 is:

Domain: {3, 4, 5, 6, 7}

Range: {7, 5, 3, 1, -1}

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step-by-step explanation: