Answer:
g(x) = 4x - 23
Explanation:
We will assume a linear function for g(x)
This will be of the form g(x) = ax + b where a and b are constants
Given the info,
g(3) = a(3) + b = -11
g(7) = a(7) + b = 5
Thus we have two equations in a and b
3a + b = -11 [1]
7a + b = 5 [2]
Subtract [1] from [2]:
7a + b - (3a + b) = 5 - (-11)
7a + b - 3a - b = 5 + 11
4a = 16
a = 4
Substitute for a in equation [2]:
4(7) + b = 5
28 + b = 5
b = 5-28 = -23
So equation of g(x) is
g(x) = 4x - 23