Answer:
f-1(x)=-[tex]\frac{2}{3}[/tex]x-[tex]\frac{16}{3}[/tex]
Step-by-step explanation:
First, switch f(x) to the variable "y".
y=-[tex]\frac{3}{2}[/tex]x-8
Next, swap "x" and "y" with each other.
x=-[tex]\frac{3}{2}[/tex]y-8
Next, lets move the denominator of 2 to the other side by multiplying both sides by 2. Your result will be...
2x=-3y-16
Now move -16 to the left side.
16+2x=-3y
To get "y" by itself, lets divide each side by -3. Our result is...
y=-[tex]\frac{2}{3}[/tex]x-[tex]\frac{16}{3}[/tex]
To finish the problem off, replace y with f-1(x) and your complete answer will be...
f-1(x)=-[tex]\frac{2}{3}[/tex]x-[tex]\frac{16}{3}[/tex]
