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The domain of a function g(x) is x > 3, and the range is y> 1. What are the
domain and range of its inverse function, g + (x)?
A. Domain: > 1
Range: y = 3
B. Domain: x <3
Ranger y < 1
C. Domain: 3
Range: y = 1
D. Domain x 1
Range 3

The domain of a function gx is x gt 3 and the range is ygt 1 What are the domain and range of its inverse function g x A Domain gt 1 Range y 3 B Domain x lt3 R class=

Respuesta :

Answer:

A.

Step-by-step explanation:

Using concepts of inverse functions, it is found that the correct option is:

A.

Domain: x > 1

Range: y > 3

  • In the inverse function, the inputs and outputs are exchanged, thus, the domain and range are also exchanged.
  • The domain of [tex]g(x)[/tex] is x > 3, thus, the range of the inverse function [tex]g^{-1}(x)[/tex] is of y > 3.
  • The range of [tex]g(x)[/tex] is y > 1, thus, the domain of the inverse function [tex]g^{-1}(x)[/tex] is of x > 1.

Thus, the correct option is:

A.

Domain: x > 1

Range: y > 3

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