Can you check my work? Thank you :)

1. The Domain of a function F is the same as the range of F^-1 (True or False?)

Answer: True.

2. Does the function y = |x-2| have an inverse? Select the best answer.

A. Yes, it passes the horizontal line test.
B. No, it does not pass the horizontal line test.
C. It's inverse is y = |x| - 2
D. It's inverse is y = |x+2|

Answer: B

3. What is the inverse of: x + 4 ?

A.x - 4
B. x + 2
C.y + 4
D. y - 2

Answer: A

4. Which statement describe the Horizontal Line Test?

A. If any horizontal line touches the function more than once, the function has an inverse.
B. If any horizontal line touches the function more than once, the function is not a function.
C. If any horizontal line touches the function only once, the function has an inverse.
D. If any horizontal line touches the function only once, the function always has real roots.

Answer: C

I agree

1. To check if the statement is true or false, you need to understand the concept of domain and range of a function. The domain of a function is the set of all possible inputs, while the range is the set of all possible outputs. The inverse of a function swaps the inputs and outputs of the original function. So, if the domain of a function F is the same as the range of its inverse, it means that the inputs of F become the outputs of its inverse, which implies that the range of F is also the domain of F^-1. Therefore, the statement is true.

2. To determine if the function y = |x-2| has an inverse, you can use the horizontal line test. The horizontal line test states that if any horizontal line intersects the graph of a function at more than one point, then the function does not have an inverse. In this case, if you draw a horizontal line at y = 0, it intersects the graph of y = |x-2| at two points, (-2, 0) and (2, 0). Therefore, the function does not pass the horizontal line test. The correct answer is B.

3. To find the inverse of the function x + 4, you need to swap the variables x and y and solve for y. So, you have y = x + 4. Then, subtract 4 from both sides to isolate x, which gives you y - 4 = x. Finally, swap x and y to get the inverse function as x - 4. Therefore, the correct answer is A.

4. The horizontal line test is a way to determine if a function has an inverse. According to the horizontal line test, if any horizontal line intersects the graph of a function more than once, then the function does not have an inverse. The reason behind this is that for a function to have an inverse, every input (x-value) must correspond to one and only one output (y-value). Therefore, if any horizontal line touches the function only once, it implies that the function has an inverse. Hence, the correct answer is C.