Respuesta :
Option C: [tex]y=\pm\frac{\sqrt{x+4}}{3}[/tex] is the inverse of the function
Explanation:
The given function is [tex]y=9 x^{2}-4[/tex]
We need to determine the inverse of the function.
To determine the inverse of the function, we need to interchange the values of x and y and solve for y.
Let us interchange the variables x and y in the function [tex]y=9 x^{2}-4[/tex], we have,
[tex]x=9 y^{2}-4[/tex]
Adding both sides of the equation by 4, we have,
[tex]x+4=9 y^{2}[/tex]
Dividing both sides of the equation by 9, we have,
[tex]\frac{x+4}{9} =y^2[/tex]
Switch sides, we have,
[tex]y^2=\frac{x+4}{9}[/tex]
Taking square root on both sides of the equation, we have,
[tex]y=\pm\frac{\sqrt{x+4}}{3}[/tex]
Thus, the inverse of the function is [tex]y=\pm\frac{\sqrt{x+4}}{3}[/tex]
Therefore, Option C is the correct answer.
