Answer: [tex]f^{-1}(x)=-\frac{2}{3}x+\frac{7}{3}[/tex]
Step-by-step explanation:
To find the inverse of a function, you want to replace x with y and y with x. Then, you solve for y.
[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex] [replace y with x and x with y]
[tex]x=-\frac{3}{2}y+\frac{7}{2}[/tex] [subtract both sides by 7/2]
[tex]x-\frac{7}{2} =-\frac{3}{2}y[/tex] [multiply both sides by -2/3]
[tex]-\frac{2}{3} (x-\frac{7}{2} )=y[/tex] [distribute]
[tex]y=-\frac{2}{3}x+\frac{7}{3}[/tex]
Now, we have our inverse function.
[tex]f^-^1(x)=-\frac{2}{3}x+\frac{7}{3}[/tex]
