1. `y=x^2+4`, find Inverse of a function

Solution:
`y=x^2+4 `

Replace all x with y and y with x.
`x=y^2+4`

Now, Solve `x=y^2+4` for y

Interchange sides
`=>y^2+4=x`

`=>y^2=x-4`

`=>y=+- sqrt(x-4)`

The solution is
`y = sqrt(x-4),y = -sqrt(x-4)`

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2. `y=(x-4)/(x+4)`, find Inverse of a function

Solution:
`y=(x-4)/(x+4) `

Replace all x with y and y with x.
`x=(y-4)/(y+4)`

Now, Solve `x=(y-4)/(y+4)` for y

Interchange sides
`=>(y-4)/(y+4)=x`

`=>y-4=x(y+4)`

`=>(y-4)-x(y+4)=0`

`=>y-4-xy-4x=0`

`=>y-xy-4-4x=0`

`=>y-xy=4+4x`

`=>y(1-x)=4+4x`

`=>y=(4*(1+x))/(1-x)`

`=>y=((4*(1+x))/(1-x))`

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