Given f(x) = k(2+x), find the value of k if f^-1 (-2) = -3

f(x) = k(2+x)

First we will
rewrite:

y= k(2+ x)

Let us determine
the inverse .

==> We will divide by
k.

==> (x+2) = y/k

==> x
= (y/k) - 2

Now we will replace x and
y.

==> y= (x/k) - 2

Then the
inverse function is given by:

f^-1 (x) = (x/k)
-2

Now given that f^-1 ( -2) =
-3

==> f^-1 (-2) = (-2/k) -2 =
-3

We will add 2 to both
sides.

==> -2/k = -1

Now we will
multiply by k.

==> -2 =
-k

==> k =
2