Inverse Functions Worksheets Grade 12

1. Dr. Rodriguez is studying the decay of a radioactive isotope in a medical application. The remaining mass M(t) in grams 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 grams. Find the inverse function M⁻¹(x) that would allow her to calculate the time required for the isotope to decay to any given mass.
2. Given f(x) = 2x + 5, sketch the graph of f and its inverse f⁻¹ on the same coordinate plane. Then, verify that the point (3, 11) on f reflects to (11, 3) on f⁻¹ across the line y = x.
3. The graph of function f(x) is a smooth curve that passes through points (-2, 16), (-1, 2), (0, 1), (1, 0.5), and (2, 0.25). The curve appears to be exponential in nature. If the inverse function f⁻¹(x) is obtained by reflecting f(x) across the line y = x, what is the value of f⁻¹(2)?

…and 4 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. The graph of function f(x) is a cubic curve that passes through points (-2, -8), (-1, -1), (0, 0), (1, 1), and (2, 8). The function appears to be strictly increasing and one-to-one. If the inverse function f⁻¹(x) is obtained by reflecting f(x) across the line y = x, what is the value of f⁻¹(1)?
3. If f(x) = 4x³ + 2 and g(x) is its inverse, then g(66) = ?

…and 4 more problems

1. A marine biologist is studying the cooling rate of ocean water after a volcanic vent becomes inactive. The temperature T(t) in degrees Celsius after t hours is modeled by the function T(t) = 80e^(-0.2t) + 15. The biologist needs to determine how many hours it will take for the water temperature to reach 35°C. Find the inverse function T⁻¹(x) that would allow the biologist to calculate the time required for any given temperature.
2. If f(x) = 9x³ + 17 and g(x) is its inverse, then g(764) = ?
3. A marine biologist is studying the cooling rate of ocean water after a volcanic vent becomes inactive. The temperature T in degrees Celsius is modeled by the function T(t) = 80e^(-0.2t) + 15, where t is time in hours. To determine how long it will take for the water to cool to a specific temperature, the biologist needs to find the inverse function. What is the inverse function T⁻¹(x) that gives the time required to reach a temperature of x degrees Celsius?

…and 4 more problems