Composite Functions Worksheets Grade 12

1. Given f(x) = √(x + 3) and g(x) = 1/(x - 1), find the domain of (f ∘ g)(x)
2. A marine biologist is studying the population dynamics of a fish species in a lake. The fish population P(t) after t years is modeled by P(t) = 1000e^(0.05t). The water quality function Q(p) = 1/(p - 800) measures how water quality depends on the fish population p. To understand how water quality changes over time, the biologist needs to find the domain of the composite function Q(P(t)). What is the domain of Q(P(t)) in this real-world context?
3. Given f(x) = √(x + 3) and g(x) = 1/(x² - 9), find the domain of (g∘f)(x)

…and 4 more problems

1. A composite function h(x) = f(g(x)) is defined where f(x) = √(x - 3) and g(x) = 1/(x - 5). On a coordinate plane, the graph of g(x) shows a vertical asymptote at x = 5, with the curve approaching positive and negative infinity on either side. The graph of f(x) begins at point (3, 0) and increases as a square root curve to the right. Determine the domain of h(x) in interval notation by analyzing the visual constraints from both functions.
2. Given f(x) = √(x + 3) and g(x) = 1/(x - 2), find the domain of (g∘f)(x)
3. Given f(x) = √(x + 3) and g(x) = 1/(x - 2), find the domain of (g∘f)(x) in interval notation.

…and 4 more problems

1. A marine biologist is modeling the growth of a bacterial colony in a nutrient solution. The population P(t) after t hours is given by P(t) = ln(t - 1), and the rate of nutrient consumption N is modeled by N(P) = 1/(P - 2), where P is the population in thousands. To understand how nutrient consumption changes over time, the biologist needs to find the domain of the composite function N(P(t)). What is the domain of N∘P?
2. Given f(x) = √(x + 3) and g(x) = 1/(x - 2), find the domain of (f ∘ g)(x)
3. A marine biologist is studying the temperature-dependent growth of a coral species. The water temperature T in degrees Celsius is modeled by T(t) = 20 + 5sin(πt/6), where t is time in months. The coral growth rate G is given by G(T) = ln(T - 15). To understand how coral growth varies over time, the biologist needs to find the domain of the composite function G(T(t)). What is the domain of this composite function?

…and 4 more problems