Answer:
[tex]f^{-1} (x)=\frac{x+6}{7}[/tex]
Step-by-step explanation:
To find the inverse of a function, we must substitute in y for f(x), swap the locations of y and x, and then solve for y
[tex]y=7x-6\\\\x=7y-6\\\\x+6=7y\\\\y=\frac{x+6}{7} \\\\f^{-1} (x)=\frac{x+6}{7}[/tex]
The inverse of the given function [tex]f^{-1}(x)=\frac{x+6}{7}[/tex].
We have given that,F(x) = 7x - 6
We have to determine the value of the inverse function.
An inverse is a function that serves to undo another function.
That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
To find the inverse of a function,
we must substitute in y for f(x), swap the locations of y and x, and then solve for y,
[tex]y=7x-6\\x=7y-6\\x+6=7y\\y=\frac{x+6}{7}[/tex]
We get the value of [tex]y=(x+6)/7.[/tex]
Taking inverse on both sides so we get,[tex]f^{-1}(x)=\frac{x+6}{7}[/tex]
Therefore the inverse of the given function [tex]f^{-1}(x)=\frac{x+6}{7}[/tex].
To learn more about the inverse function visit:
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