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A function and its inverse are shown on the same graph. Which statement describes the relationship between the function and its inverse? The slope of f–1(x) is the same as the slope of f(x). The slope of f–1(x) is the opposite as the slope of f(x). The x-intercept of f–1(x) is the same as the y-intercept of f(x). The x-intercept of f–1(x) is the opposite as the y-intercept of f(x).

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Answer:

C) The x-intercept of f–1(x) is the same as the y-intercept of f(x).

Step-by-step explanation:

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(C) The x-intercept  [tex]f-1(X)[/tex]  is the same as the y-intercept [tex]f(X)[/tex].

Function:

  • A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X.
  • The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

The inverse of a function:

  • An inverse in mathematics is a function that "undoes" another function.
  • In other words, if [tex]f(X)[/tex] produces y, then y entered into the inverse of f makes x.
  • An invertible function is one that has an inverse, and the symbol [tex]f1[/tex] represents the inverse.

Therefore, the correct answer is (C) the x-intercept  [tex]f-1(X)[/tex]  is the same as the y-intercept [tex]f(X)[/tex].

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