Answer:
[tex]-\frac{x}{2} - 3[/tex]
Explanation:
d(x) = -2x - 6
to find the inverse of a function, you need to follow these steps:
1. set d(x) = y
2. interchange the variables, so y becomes x and x becomes y
3. solve the equation for y
step 1: set d(x) = y
y = -2x -6
step 2: interchanging the variables
y = -2x - 6 turns into x = -2y - 6
step 3: solving for y
x = -2y - 6 < add 6 to both sides to get rid of it on the right
x + 6 = -2y < divide both sides by -2 to get y alone
x + 6 / -2 = [tex]-\frac{x}{2} - 3[/tex]
-2y / -2 = y
[tex]-\frac{x}{2} - 3[/tex] = y
so the inverse of the function is [tex]-\frac{x}{2} - 3[/tex]
