Respuesta :
The inverse function returns the original value for which the output of a function was given.
[tex]y^{-1}[/tex] = -1 ± √(x - 5) /2 be the inverse the function y = (1 - 2x)² + 5.
What is the inverse formula?
The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value. The inverse of f is then g(y) = (y - 5)/2 = x.
An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.
Let the equation be y = (1 - 2x)² + 5
simplifying the above equation, we get
√(x - 5) y = (1 - 2x)² + 5
x = (1 - 2y)² + 5
The function of x be x = (1 - 2y)² + 5
x - 5 = (1 - 2x)²
± √(x - 5) = (1 - 2y)
± √(x - 5) - 1 = 2y
Divide both sides of the equation by 2, we get
[± √(x - 5) - 1]/2 = 2y/2
[± √(x - 5) -1] /2 = y
[tex]y^{-1}[/tex] = -1 ± √(x - 5) /2
Therefore, the inverse of the function be [tex]y^{-1}[/tex] = -1 ± √(x - 5) /2.
To learn more about inverse formula refer to:
https://brainly.com/question/10219387
#SPJ4
