Answer:
[tex](3) f\f^{-1} (x)=-\frac{1}{6}x+\frac{1}{12}[/tex]
Step-by-step explanation:
Inverse is basically finding [tex]x[/tex] in terms of [tex]y[/tex].
Let [tex]y = -6x+\frac{1}{2}[/tex]
[tex]y = -6x+\frac{1}{2}\\\\y-\frac{1}{2}=-6x\\\\6x =-y+\frac{1}{2} \\\\x=-\frac{1}{6}y+\frac{1}{12} \\\\f^{-1} (x)=-\frac{1}{6}x+\frac{1}{12}[/tex]
Hence, answer is [tex](3)\ f^{-1} (x)=-\frac{1}{6}x+\frac{1}{12}[/tex]