Inverse Functions Worksheets Grade 12

1. Given f(x) = (1/6)x³ + 1, sketch the graph of f and its inverse f⁻¹ on the same coordinate plane. Verify that the point (6, 37) on f reflects to (37, 6) on f⁻¹ across the line y = x.
2. If f(x) = 7x³ + 2 and g(x) is its inverse, then g(247) = ?
3. Dr. Rodriguez is studying the cooling rate of a chemical compound in her laboratory. The temperature T(t) in degrees Celsius after t minutes is modeled by the function T(t) = 80e^(-0.05t) + 20. She needs to determine how long it will take for the compound to cool to 40°C. Find the inverse function T⁻¹(x) that would allow her to calculate the time required to reach any given temperature x.

…and 6 more problems

1. If f(x) = 12x³ + 19 and g(x) is its inverse, then g(175) = ?
2. Aroha is a volcanologist studying the cooling of lava after an eruption. The temperature T(t) in degrees Celsius of a lava sample t hours after collection is modeled by the function T(t) = 35 + 45e^(-0.15t) for t ≥ 0. Aroha wants to create a graph that shows both the original function and its inverse to better understand how temperature and time are related. She knows the inverse function will be a reflection of T(t) across the line y = x. Find the inverse function T⁻¹(x) that gives the time in hours required for the lava to cool to any given temperature x degrees Celsius.
3. Liam is analyzing the temperature fluctuations in a chemical reaction. The temperature T(t) in degrees Celsius at time t hours is modeled by the function T(t) = 3t² - 12t + 15 for t ≥ 0. Liam wants to determine at what time the temperature reaches a specific value. If the inverse function exists for the domain t ≥ 2, find T⁻¹(15).

…and 3 more problems

1. Dr. Rodriguez is studying the decay of a radioactive isotope in a medical application. The remaining mass M(t) in milligrams after t days is modeled by the function M(t) = 80e^(-0.0231t). She needs to determine how many days it will take for the isotope to decay to 20 milligrams. Find the inverse function M⁻¹(x) that would allow her to calculate the time required for the isotope to reach any given mass.
2. Given f(x) = 6x³ + 11 and g(x) is its inverse, then g(491) = ?
3. If f(x) = 4x³ + 11 and g(x) is its inverse, then g(75) = ?

…and 4 more problems