Question

Determine whether the following function is a​ one-to-one function. If it is​ one-to-one, list the inverse function by switching​ coordinates, or inputs and outputs. f={(9,7), (7,9), (6,7)} (1 point) The function f is not a one-to-one function. The function is one-to-one. The inverse is f−1={(−9,7), (−7,9), (−6,7)}. The function is one-to-one. The inverse is f−1={(−7,−9), (−9,−7), (−7,−6)}. The function is one-to-one. The inverse is f−1={(7,9), (9,7), (7,6)}.

Answer 1

The function f={(9,7), (7,9), (6,7)} is a one-to-one function, and the inverse function is f^{-1}={(7,9), (9,7), (7,6)}.

Step-by-step explanation:

To determine whether the function f={(9,7), (7,9), (6,7)} is a one-to-one function, we must check if each input (first component of each ordered pair) maps to exactly one unique output (second component of each ordered pair). In this case, the function does map each input to a unique output, therefore the function is one-to-one.

Next, finding the inverse of the function involves swapping the inputs and outputs. This means flipping each pair: the first component becomes the second, and the second component becomes the first. Therefore, the inverse function is f-1={(7,9), (9,7), (7,6)}.

Answer 2

Answer: An easy way to determine whether a function is a one-to-one function is to use the horizontal line test on the graph of the function. To do this, draw horizontal lines through the graph. If any horizontal line intersects the graph more than once, then the graph does not represent a one-to-one function.

i dont know the exact answer but its a lil sum

Step-by-step explanation:

We know that for any two inverses f(x) = g(y), meaning that if we take f(x) for any x in the domain of f(x), then g(y), where y is the outcome of f(x), should output x. So that is a simple test to see if two functions are inverses.