Question

Find the inverse function of h(x) = - 2/3x + 6.

Answer 1

To find the inverse function, interchange the variables and solve for y.
h^-1 (x) = -9 - 3x/2

Answer 2

Answer:

y = $-\frac{3}{2} x - 9$

Step-by-step explanation:

The given function h(x) = $-\frac{2}{3} x + 6$

To find the inverse function, we have to do the following steps:

Step 1: Replace h(x) by "x" and "x" by "y"

x = $-\frac{2}{3} y + 6$

Step 2: Write the function y interms of x.

Subtract 6 from both sides, we get

$x - 6 = -\frac{2}{3} y + 6 - 6$

$x - 6 = -\frac{2}{3} y$

Multiply both sides by the reciprocal of -2/3.

The reciprocal of -2/3 is -3/2.

$-\frac{3}{2} (x - 6) = -\frac{3}{2} *-\frac{2}{3} *y$

y = $-\frac{3}{2} x -\frac{3}{2} *6$

$y = -\frac{3}{2} x - 9$

The inverse function y = $-\frac{3}{2} x - 9$