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If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?

On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).


A.(0, –2)
B.(1, –1)
C.(2, 0)
D.(3, 3)

Respuesta :

Answer:

Step-by-step explanation:

3,3

The point of intersection of f(x) and  [tex]f^{-1}(x)[/tex]  is (3, 3)

The correct answer is an option (D)

What is a function?

  • "It defines a relation between input and output values."
  • "In function, for each input there is exactly one output."

What is inverse function?

"The inverse function of x = f(m) is m =  [tex]f^{-1}(x)[/tex], where x, m are real values"

For given question,

A function  f(x) and its inverse function, [tex]f^{-1}(x)[/tex] are both plotted on the same coordinate plane.

We know that the inverse function  [tex]f^{-1}(x)[/tex] is the mirror image of the function f(x.)

This means, both the functions must be symmetric about the line y = x.

The curve of inverse function  [tex]f^{-1}(x)[/tex] would cross the Y-axis at (0, 2), changes direction at (-1, -1) and crosses the X-axis at (-2, 0)

And both the functions intersect each other only on y = x

The point which satisfy the line y = x is (3, 3)

Therefore, the point of intersection of f(x) and  [tex]f^{-1}(x)[/tex]  is (3, 3)

The correct answer is an option (D)

Learn more about inverse function here:

https://brainly.com/question/2541698

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