What is the inverse function of h(x) = -2/3x + 6?

Solution:

Given: Function h(x) = -2/3 x + 6

Now we have to find the inverse of the given function.

Step 1 :  Let the given function be y.

⇒ h(x) = y

⇒ y = -2/3 x + 6

Step 2 : Now interchange x and y

⇒ x = -2/3 y + 6

Step 3 : Now solve the equation for y

⇒ x = -2/3 y + 6

⇒ x - 6 = -2/3 y

⇒ (x - 6 ) 3 = (-2) y

⇒ 3x - 18 = -2y

⇒ (3x - 18 )/-2 = y

⇒ y = (3x - 18)/-2

Since we swapped x and y we have y = h⁻¹(x)

h⁻¹(x) =(3x -18)/-2

---

What is the inverse function of h(x) = -2/3x + 6?

Summary:

The inverse of the function h(x) = -2/3 x + 6 is h⁻¹(x) = (3x -18)/-2.