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)`
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))`
This material is intended as a summary. Use your textbook for detail explanation.
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