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

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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**