Final answer:
The solutions of the equation f(x)=g(x) are the x-values at which the two functions have equal outputs, signifying their intersection points. Inversely, if f(x)g(x) equals a constant, f(x) and the multiplying factor are inversely proportional. With quadratic equations, two solutions usually exist, but real-world context may deem one more reasonable.
Step-by-step explanation:
The statement "Which statement is true about the solutions of the equation f(x)=g(x)?" suggests that we are dealing with an equation where two functions, f(x) and g(x), are set equal to each other. The solutions to this equation are the x-values for which both functions have the same output, or y-value. In other words, these are the intersection points of the graphs of f(x) and g(x).
When discussing the solutions to f(x)g(x) = constant, where the product of f(x) and some value λ equals a constant, we're exploring inverse variation. As f(x) gets smaller, λ must get larger to maintain the constant product, and as f(x) gets larger, λ must get smaller. This relationship is fundamental to understanding direct and inverse variation.
In the context of quadratic equations, where the function includes an unknown squared, there are typically two solutions. However, in applied problems, sometimes only one solution is practically significant. Recognizing which solution(s) make sense within real-world constraints is an essential part of problem-solving.