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The domain of a function f(x) is x> 1, and the range is y< -2. What are the
domain and range of its inverse function, f-1 (x)?
A. Domain: x> 1
Range: y< -2
B. Domain: x>-2
Range: ys 1
C. Domain: x< -2
Range: y> 1
O D. Domain: xs1
Range: y> -2

Respuesta :

Answer: Choice C

Domain:  x < -2

Range: y > 1

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Explanation:

When going from the original function [tex]f(x)[/tex] to its corresponding inverse [tex]f^{-1}(x)[/tex], or vice versa, the roles of x and y swap places. The inverse undoes whatever the original function does.

This swap means that the domain and range also swap as well. The original domain x > 1 becomes the range y > 1 for the inverse. The range y < -2 in the original becomes x < -2 which is the domain of the inverse.

facundo3141592

The domain and range of the inverse functions are:

  • domain: x < - 2
  • range: y > 1.

What are the domain and range of the inverse function?

We know that two functions are inverses if:

f( g(x)) = x

g( f(x)) = x

So, the domain of f(x) is the range of g(x), and the range of f(x) is the domain of g(x).

Then the domain and range of the inverse function are:

  • domain: x < - 2
  • range: y > 1.

If you want to learn more about domain and range:

https://brainly.com/question/10197594

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