Answer:
[tex]{f}^{ - 1} (x) = \frac{x + 6}{2} \\ [/tex]
Step-by-step explanation:
[tex]f(x) = 2x-6[/tex]
To find the inverse of f(x) , equate f(x) to y that's
[tex]y = 2x - 6[/tex]
Next interchange the terms that's x becomes y and y becomes x
[tex]x = 2y - 6[/tex]
Next solve for y
Move 6 to the other side of the equation
That's
[tex]2y = x + 6[/tex]
Divide both sides by 2 to make y stand alone
[tex] \frac{2y}{2} = \frac{x + 6}{2} \\ \\ y = \frac{x + 6}{2} [/tex]
We have the final answer as
[tex] {f}^{ - 1} (x) = \frac{x + 6}{2} \\ [/tex]
Hope this helps you
