Answer:
[tex]f(x)=\frac{1-7x}{-x-5}[/tex]
Step-by-step explanation:
The inverse of a function can be easily calculated isolating Y and then changing the variables ( X by Y and viceversa).
So we are going to isolate Y from our equation: [tex]y=\frac{5x+1}{-x+7} \\y. (-x+7)=5x+1 \\\\-xy+7y=5x+1\\-xy-5x=1-7y\\x. (-y-5) = 1-7y\\x=\frac{1-7y}{-y-5}\\ \\[/tex]
Now we change the variables and we get:
[tex]f(x)=\frac{1-7x}{-x-5}[/tex]
