Function Inverses Worksheets Grade 12

1. A function f(x) = 2x + 3 is graphed on a coordinate plane. Its inverse function f⁻¹(x) is reflected across the line y = x. If you compose these functions by following the graph of f from point (1,5) to the line y = x, then following the reflection to f⁻¹, what is the resulting coordinate point after this composition?
2. f(x) = 2x + 3 and g(x) = (x - 3)/2, find f(g(5)) = ?
3. A function f(x) = (x - 2)³ + 1 is graphed on a coordinate plane. Its inverse function f⁻¹(x) is also graphed, reflected across the line y = x. If you start at the point (3, 2) on f(x) and follow this path: move horizontally to the line y = x, then vertically to f⁻¹(x), what are the coordinates of the final point reached on f⁻¹(x)?

…and 4 more problems

1. Sophia is an astrophysicist modeling the temperature of a star as a function of its core pressure. She defines the temperature function f(x) = 6x - 11, where x represents pressure in megapascals, and the pressure function g(x) = (x + 11)/6. Sophia needs to verify that these two functions are inverses of each other by checking that f(g(x)) = x and g(f(x)) = x for all real x. Perform the composition tests and determine if f and g are indeed inverse functions.
2. Given f(x) = 5x - 12 and g(x) = (x + 12)/5, verify f(g(23)) = ?
3. Mason is an aerospace engineer designing a satellite's thermal control system. The temperature regulation is modeled by two functions: f(x) = 4x - 9 and g(x) = (x + 9)/4, where x represents the electrical current in amperes. To verify that these functions are inverses, Mason must show that f(g(x)) = x and g(f(x)) = x. Perform these compositions and determine whether f and g are inverse functions.

…and 4 more problems

1. Kaia is a hydrologist modeling the flow rate of a river after a storm. The flow rate in cubic meters per second is given by the function f(x) = 4x - 9, where x is the water level in meters above flood stage. Her colleague Tane proposes that the inverse function is g(x) = (x + 9)/4. Using function composition, verify whether f(x) and g(x) are inverse functions by computing f(g(x)) and g(f(x)).
2. Given f(x) = 7x³ + 2 and g(x) = ∛((x - 2)/7), verify f(g(37)) = ?
3. A function f(x) = 2x - 5 is graphed on a coordinate plane. Its inverse function f⁻¹(x) is reflected across the line y = x. If you compose these functions by following the path from point (7,9) on f(x) horizontally to the line y = x, then vertically to f⁻¹(x), what are the coordinates of the final point on f⁻¹(x)?

…and 4 more problems