Respuesta :

Ben

[tex]\huge\boxed{\text{The first graph}}[/tex]

A good way to determine if a line represents a valid function is to use the vertical line test.

To do this, you imagine a vertical (up and down) line moving across your graph from left to right. It should only be touching the line at one point at a time.

If it is touching more than one point on the line at a time, the line is not a valid function.

The first line and its inverse both pass the test.

The second line passes the test, but its inverse does not.

The third line also passes the test, but again, its inverse does not.

The same applies to the fourth line and its inverse.

Using the concept of inverse function, it is found that the first graph shows a function whose inverse is also a function.

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A function f(x) will only have an inverse function if: [tex]f(a) = f(b) \leftrightarrow a = b[/tex], that is, a value of y will have only one respective value of x.

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  • In the first graph, for each value of y, there is only one value of x, so the inverse is also a function, and this is the correct option.
  • In the second graph, for example, y = 0 when x = -1 and when x = 1, so the inverse is not a function.
  • In the third graph, for example, y = -3 when x = 0 and x = 2, so the inverse is not a function.
  • In the fourth graph, for example, y = 1 for two values of x, so the inverse is not a function.

A similar problem is given at https://brainly.com/question/23339681

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