Question

What is the inverse of the given function?

Answer 1

Answer: -7, -1, 5, -5

Explanation:

In order to find the inverse, swap the x's and y's and solve for y.

`y=(5x+1)/(-x+7)\\\\\\\underline{Swap\ the\ x's\ and\ y's}:\\x=(5y+1)/(-y+7)\\\\\\\underline{\text{Multiply both sides by -y+1 to clear the denominator}}:\\x(-y+7)=5y+1\\-xy+7x=5y+1\\\\\\\underline{\text{Add xy and subtract 1 from both sides}}:\\7x-1=xy+5y\\\\\\\underline{\text{Factor out the y from the right side}}:\\7x-1=y(x+5)\\\\\\\underline{\text{Divide x+5 from both sides}}:\\(7x-1)/(x+5)=y`

Since the boxes you need to fill in show -x in the denominator, multiply the equation by -1/-1:

`y=(-1)/(-1)\bigg((7x+1)/(x+5)\bigg)\\\\\\\large\boxed{f^(-1)(x)=(-7x-1)/(-x-5)\qquad for\ x \\eq -5}`