Question

The two functions f(x) and g(x) are linearly dependent. Fill in the missing values:

f(8) = -6
g(8) = 10.8
f(14) = 6
g(14) =?

Answer 1

The missing value, g(14), can be found by expressing one function in terms of the other using the given values. Using the slope formula and the known value of f(8), we can solve for the missing value.

Step-by-step explanation:

Since the functions f(x) and g(x) are linearly dependent, we can express one in terms of the other. Let's find the equation of the line represented by f(x) and g(x) using the given values:

First, we find the slope of the line using the formula:

slope = (g(8) - g(14)) / (8 - 14) = (10.8 - ?) / (8 - 14)

Using the value of f(8) = -6, we can substitute it into the equation:

-6 = (f(8) - ?) / (8 - 14)

Solving for ?, we get ? = -25.8

Therefore, g(14) = -25.8.