Question

Given f(x) = k(4+2x) find the value of k if f^-1( 6)=1

Answer 1

Using the inverse function, it is found that the value is of k = 1.

How to find the inverse function?

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:

$y = k(4 + 2x)$

Exchanging x and y, and isolating y:

$x = k(4 + 2y)$

$4k + 2ky = x$

$2ky = x - 4k$

$y = \frac{x - 4k}{2k}$

$f^{-1}(x) = \frac{x - 4k}{2k}$

f^-1(6)=1, hence:

$f^{-1}(x) = \frac{x - 4k}{2k}$

$1 = \frac{6 - 4k}{2k}$

$6 - 4k = 2k$

$6k = 6$

$k = \frac{6}{6}$

$k = 1$

More can be learned about inverse functions at brainly.com/question/8824268