1. `y=sqrt(x-8)`, find Domain of a function
Solution:
`y=sqrt(x-8)`
`x-8>=0`
`=>x-8>=0`
`=>x>=0+8`
`=>x>=8`
Domain : `x>=8`
Domain set is
Interval Notation : `[8,oo)`
Set-Builder Notation : `x>=8`
2. `y=sqrt(x+2)/(x^2-9)`, find Domain of a function
Solution:
`y=sqrt(x+2)/(x^2-9)`
`x+2>=0`
`=>x+2>=0`
`=>x>=0-2`
`=>x>=-2`
`x^2-9=0`
`=>x^2-9=0`
`=>x^2=0+9`
`=>x^2=9`
`=>x=+- 3`
Domain : `x!=3,x!=-3`
Domain set is
Interval Notation : `[-2,3)uu(3,oo)`
Set-Builder Notation : `-2<=x< 3 or x>3`
This material is intended as a summary. Use your textbook for detail explanation.
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