Inverse Functions Worksheets Grade 12

1. A function is represented graphically as a cubic curve with points at (-2, -11), (0, 1), and (1, 4). The function is defined as f(x) = ax³ + bx² + cx + d. Find the algebraic expression for the inverse function f⁻¹(x) and evaluate f⁻¹(4).
2. f(x) = (2x - 3)/(x + 1), find f⁻¹(x) = ?
3. f(x) = (4x + 1)/(2x - 3), find f⁻¹(x) = ?

…and 5 more problems

1. f(x) = (2x - 5)/(x + 3), find f⁻¹(x) = ?
2. A biomedical company is modeling the concentration of a new medication in a patient's bloodstream using the function C(t) = (2t + 3)/(t - 1), where C represents concentration in mg/L and t represents time in hours. To determine when the concentration reaches a specific level, they need to find the inverse function. What is the inverse function t(C) that gives the time when the concentration is C mg/L?
3. f(x) = (11x + 17)/(8x - 15). Find f⁻¹(x) = ?

…and 4 more problems

1. Hana is a marine biologist modeling the water temperature in a geothermal vent ecosystem. The temperature T(d) in degrees Celsius at depth d meters below the ocean surface is given by the function T(d) = (12d + 15)/(d + 3). To determine the depth at which a specific temperature occurs, Hana needs to find the inverse function. What is the inverse function d(T) that gives the depth in meters when the temperature is T degrees Celsius?
2. A biomedical company is modeling the concentration of a new drug in a patient's bloodstream using the function C(t) = (2t + 3)/(t - 1), where C is the concentration in milligrams per liter and t is time in hours. To determine when the drug concentration reaches a specific level, the researchers need to find the inverse function. Find the inverse function t(C) that gives the time when the concentration equals C.
3. A function is represented graphically as a cubic curve with inflection point at (1, 2) and passing through points (0, 3) and (2, 1). The function has the form f(x) = a(x - h)³ + k. Find the algebraic expression for its inverse function f⁻¹(x).

…and 4 more problems