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 = \(-\frac{3}{2} x - 9\)
