Respuesta :

Answer: [tex]f^{-1}(x) = \frac{x-1}{8}[/tex]

Step-by-step explanation:

Given:

[tex]f(x) = 8x +1[/tex]

First step: Let f(x) be y, the function then becomes

[tex]y = 8x + 1[/tex]

Step 2: Make x the subject of the formula: That is

[tex]8x = y + 1[/tex]

[tex]x = \frac{y-1}{8}[/tex]

Step 3: Replace x with [tex]f^{-1}(x)[/tex]  and y with x.

Therefore:

[tex]f^{-1}(x) = \frac{x-1}{8}[/tex]

The inverse of the function f(x)=8x+1 is;

  • f-¹(x) = (x - 1)/8

The function can be written as y = 8x + 1 for evaluation.

By making x the subject of the function; we have;

  • x = (y - 1)/8

By swapping x and y; we have;

  • y = (x - 1)/8

Ultimately, the inverse of the function is; f-¹(x)=8x+1

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