The graph below shows the function y = 3^x + 1, with a restricted domain.

Which of the following correctly shows the domain and range of the inverse of this function?

1. Domain {x|x ≥ 2}
   Range   {y|y ≥ 0}
   Correct! The domain of the inverse function will be all possible y-values of the given function and the range will be all possible x-values of the given function.
2. Domain {x|x ≥ 0}
   Range   {y|y ≥ -2}
   Incorrect. The domain of the inverse function will be the range of the given function.
3. Domain {x|x ≥ 0}
   Range   {y|y ≥ 2}
   Incorrect. This is the domain of the given function not the inverse function.
4. Domain {x|x ≤ 0}
   Range   {y|y ≥ 2}
   Incorrect. The domain of the inverse function will be the range of the given function.

An exponential function with a restricted domain is shown on the graph below.

Which of the following correctly shows the domain and range of the inverse of this function?

1. Domain {x|x ≥ 2}
   Range   {y|y ≥ 0}
   Incorrect. The domain contains all possible x-values.
2. Domain {x|x ≥ -2}
   Range   {y|y ≥ 0}
   Correct! The domain of the inverse function will be the range of the given function and the range of the inverse function will be the domain of the given function.
3. Domain {x|x ≥ 0}
   Range   {y|y ≥ -2}
   Incorrect. This is the domain and range of the original function.
4. Domain {x|x ≤ -2}
   Range   {y|y ≥ 0}
   Incorrect. The domain contains numbers greater than –2 and the range contains numbers greater than zero.

The graph of an exponential function with a restricted domain, f(x), is shown below. The graph of the inverse of the function, f ^-1(x), is also shown.

Which of the following is a true statement about the function and its inverse?

1. The domain of f(x) contains the same values as the range of f ^-1(x).
   Correct! The domain of the given function is the range of the inverse of the function.
2. The range of f(x) contains the same values as the range of f ^-1(x).
   Incorrect. The range of f(x) contains all positive numbers greater than 3.
3. The domain of f(x) contains the opposite values as the range of f ^-1(x).
   Incorrect. The domain of f(x) contains all positive values.
4. The range of f(x) can not be determined.
   Incorrect. The range of f(x) contains all positive numbers greater than 3.

The graph of a function is shown below.

Which of the following represents the range of the inverse of the function?

1. {y|y < 1.5}
   Incorrect. The range only contains positive values.
2. {y|y < 0}
   Incorrect. The range contains positive values.
3. {y|y > 1.5}
   Incorrect. This is the range of the original function.
4. {y|y > 0}
   Correct! The domain of the given function will be the range of the inverse function.

The graph of a function is shown below.

Which of the following represents the range of the inverse of the function?

1. {y|y > 1}
   Correct! The range of the inverse of the function is the domain of the given function.
2. {y|y < 1}
   Incorrect. The range only contains positive values.
3. {y|y < 0}
   Incorrect. This is the range of the original function.
4. {y|y > 0}
   Incorrect. The range does not contain numbers between 0 and 1.