fatnessrosas fatnessrosas
  • 13-05-2021
  • Mathematics
contestada

The function f(x) = 9x +5 is one-to-one.
Find an equation for f-'(x), the inverse function.

Respuesta :

joaobezerra joaobezerra
  • 18-05-2021

Answer:

The inverse function is [tex]f^{-1}(x) = \frac{x - 5}{9}[/tex]

Step-by-step explanation:

Inverse function:

Suppose we have a one-to-one function y = f(x). To find it's inverse, we exchange y and x, and then isolate y.

In this question:

[tex]y = 9x + 5[/tex]

Exchanging x and y:

[tex]x = 9y + 5[/tex]

Isolating y:

[tex]9y = x - 5[/tex]

[tex]y = \frac{x - 5}{9}[/tex]

[tex]f^{-1}(x) = \frac{x - 5}{9}[/tex]

The inverse function is [tex]f^{-1}(x) = \frac{x - 5}{9}[/tex]

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