Answer:
y = [tex]-\frac{3}{2} x - 9[/tex]
Step-by-step explanation:
The given function h(x) = [tex]-\frac{2}{3} x + 6[/tex]
To find the inverse function, we have to do the following steps:
Step 1: Replace h(x) by "x" and "x" by "y"
x = [tex]-\frac{2}{3} y + 6[/tex]
Step 2: Write the function y interms of x.
Subtract 6 from both sides, we get
[tex]x - 6 = -\frac{2}{3} y + 6 - 6[/tex]
[tex]x - 6 = -\frac{2}{3} y[/tex]
Multiply both sides by the reciprocal of -2/3.
The reciprocal of -2/3 is -3/2.
[tex]-\frac{3}{2} (x - 6) = -\frac{3}{2} *-\frac{2}{3} *y[/tex]
y = [tex]-\frac{3}{2} x -\frac{3}{2} *6[/tex]
[tex]y = -\frac{3}{2} x - 9[/tex]
The inverse function y = [tex]-\frac{3}{2} x - 9[/tex]
