[tex] f(x) = 7x -\frac{1}{2} [/tex]
replace f(x) by y
[tex] y=7x -\frac{1}{2} [/tex]
Now to find the inverse of the function replace x with y and y with x , i.e. interchange x and y
[tex] x=7y -\frac{1}{2} [/tex]
Now we have to solve for y
So add [tex] \frac{1}{2} [/tex] to both sides
[tex] x+\frac{1}{2} = 7y [/tex]
Now divide both sides by 7
[tex] \frac{x}{7} +\frac{\frac{1}{2}}{7} = y [/tex]
[tex] \frac{x}{7} +\frac{1}{14} = y [/tex]
or
[tex] y=\frac{x}{7} +\frac{1}{14} [/tex]
or
[tex] f^{-1}(x) =\frac{x}{7} +\frac{1}{14} [/tex]
