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 = [tex]\frac{-1}{3}[/tex]
We then solve for 'b':
5a + b = 9
5(-1/3) + b = 9
b = 9 + 5/3
b = 32/3 = [tex]11\frac{1}{3}[/tex].
We then use this to find A, B, C.
f(x) = (-1/3)x + 32/3
(2)
f(A) = -A/3 + 32/3 = 7
[tex]\frac{-A}{3} + \frac{32}{3} = 7\\A - 32 = -21\\A = 11[/tex]
(3)
f(7) = -7/3 + 32/3 = B
25/3 = B
(4)
f(C) = -C/3 + 32/3 = 11
[tex]\frac{-C}{3} + \frac{32}{3} = 11\\C - 32 = -33\\C = -1[/tex]
