Final answer:
To ensure that f(x) = (-5/2)x - 3 and g(x) intersect exactly once, g(x) should have a different slope and/or y-intercept than f(x). An example of such a function is g(x) = x - 3, which has a slope of 1 and the same y-intercept, ensuring a single point of intersection.
Step-by-step explanation:
To create a linear function g(x) such that f(x) = g(x) has exactly one solution, we need to find a linear equation with a different slope or y-intercept than f(x) = (-5)/(2)x - 3. Since the slope of f(x) is -5/2, choosing any slope other than -5/2 for g(x) will ensure that they intersect at exactly one point, unless they are parallel. If the y-intercepts are also different, g(x) and f(x) cannot be parallel.
Therefore, an example of a function g(x) that meets these conditions could be g(x) = x - 3, which has a slope of 1 and the same y-intercept as f(x), ensuring one point of intersection.
If f(x) has a slope of -5/2, we can be sure that any other linear function with a slope not equal to -5/2 will only intersect with f(x) at one point, given they are not parallel. This means we can select any value for the slope of g(x) that is not -5/2 to fulfill the condition of a single intersection.
A simple selection, as mentioned above, for the slope could be 1, 2, or any other value. Similarly, we can also choose a different y-intercept for g(x), other than -3, to ensure that the lines are not the same and thus intersect exactly once.