Practice with Inverses Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

Solve the following problems dealing with inverses.

 1. Is {(2,5), (7,3)} the inverse relation of the function {(5,2), (3,7)}? Choose: Yes No Explanation The x and y coordinates from the original function swap places in the inverse.

 2. Given function f, is the inverse also a function? Choose: Yes No Explanation Since function f is a one-to-one function, the inverse will also be a function.

 3. True or False:  The inverse of the graph shown below will be a function. Choose: True False Explanation This graph fails the horizontal line test. The inverse of this graph will NOT be a function.

 4. True or False:  Since f (x) is a reflection of g(x), g(x) is also the inverse of f (x). Choose: True False Explanation A graph and its inverse are reflections over the identity line (y = x), not over the x-axis.

 5. True or False:  The straight line graphs shown below are inverses of one another. Choose: True False Explanation Yes. It can be seen from observing points on the graph that the x and y coordinates have swapped places. It can also be seen that the graphs are reflections over the identity line y = x.

 6. Find Choose: 0 5 cannot be determined Explanation A function composed with its inverse function returns the starting value.

 7. True or False:  The graphs of sin(x) and cos(x) are inverses of one another. Choose: True False Explanation No. The sin(x) is not the reflection of the cos(x) over the identity line y = x.

 8. The natural logarithmic function is the inverse function of the exponential function.  Since the point (0,1) lies on the exponential function, we know that the point _____ lies on the logarithmic function. Choose: (0,1) (1,1) (1,0) Explanation The x and y coordinates from the original function swap places in the inverse function.

 9. Find the inverse for the function y = 4x + 12. Choose: Explanation 1. Set = to y 2. Interchange x and y. 3. Solve for y

 10. Find the inverse for the function Choose: Explanation 1. Set = to y 2. Swap variables. 3. Solve for y Take the cube root of both sides. Subtract 2 from both sides.

 11. Find the inverse for the function (where x is not zero). Choose: Explanation See the lesson page for a sample of this solution.

 12. Using composition of functions, show that f (x) = 2x - 3   and   g(x) = 0.5x + 1.5 are inverse functions. Answer A function composed with its inverse function yields x. f(g(x)) = f(.5x+1.5) = 2(.5x + 1.5) - 3 = x + 3 - 3 = x

 Topic Index | Algebra2/Trig Index | Regents Exam Prep Center Created by Donna Roberts