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Answer:
A = 11, B = 25/3, C = -1
Step-by-step explanation:
A linear function has the form:
f(x) = ax + b
(1)
f(3) = 8a + b = 8
f(5) = 5a + b = 9
Using the last 2 equations we can solve for 'a' and 'b'.
8a + b = 8 | 5a + b = 9
We multiply the second one by -1:
8a + b = 8 | -5a -b = -9
And then we add them together:
3a = -1
a =
We then solve for 'b':
5a + b = 9
5(-1/3) + b = 9
b = 9 + 5/3
b = 32/3 = .
We then use this to find A, B, C.
f(x) = (-1/3)x + 32/3
(2)
f(A) = -A/3 + 32/3 = 7
(3)
f(7) = -7/3 + 32/3 = B
25/3 = B
(4)
f(C) = -C/3 + 32/3 = 11