Using the inverse function, it is found that the value is of k = 1.
Suppose we have a function y = f(x).
To find the inverse, we exchange the instances of x and y, and then we isolate y.
In this problem, the function is:
[tex]y = k(4 + 2x)[/tex]
Exchanging x and y, and isolating y:
[tex]x = k(4 + 2y)[/tex]
[tex]4k + 2ky = x[/tex]
[tex]2ky = x - 4k[/tex]
[tex]y = \frac{x - 4k}{2k}[/tex]
[tex]f^{-1}(x) = \frac{x - 4k}{2k}[/tex]
f^-1(6)=1, hence:
[tex]f^{-1}(x) = \frac{x - 4k}{2k}[/tex]
[tex]1 = \frac{6 - 4k}{2k}[/tex]
[tex]6 - 4k = 2k[/tex]
[tex]6k = 6[/tex]
[tex]k = \frac{6}{6}[/tex]
[tex]k = 1[/tex]
More can be learned about inverse functions at https://brainly.com/question/8824268
