Answer:
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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