Final Answer:
The given statement "The function ƒ(x) is a linear function, and g(x) is a rational function. There is a solution to the equation ƒ(x) = g(x) between x = 3 and x = 4 that must be closer to 3 than 4." is True
Thus option a is correct.
Step-by-step explanation:
A linear function is of the form ƒ(x) = mx + c, while a rational function can be expressed as g(x) = p(x) / q(x), where p(x) and q(x) are polynomials. Since the problem doesn't specify the exact forms of ƒ(x) and g(x), we consider the general forms within the defined range to ascertain the solution.
To address this, let's consider the nature of linear and rational functions. Linear functions have a constant slope, while rational functions can have varying behaviors. For a solution between x = 3 and x = 4 closer to 3 than 4, the linear function's slope must be such that it intersects with the rational function closer to x = 3.
Given the conditions, it is possible for a linear function with a specific slope and a rational function to intersect between x = 3 and x = 4, closer to x = 3 than x = 4. The relative positioning of the graphs and their specific equations will determine this, but based on the properties of these functions, it's feasible to have a solution closer to x = 3 in this scenario.
Therefore option a is correct.