Question

Are there any restrictions on the domain of `\frac { b - 3} { - b ^ { 2} + 18b - 80} \cdot \frac { b ^ { 2} - 18b + 80} { 9b }`?

Answer 1

`b !=0, 8, 10`
`therefore b in RR-{0, 8, 10}`

Explanation:

Since the denominator cannot have `0`, we can find the restrictions on the domain in the following way.

`9b != 0`
`implies b!= 0`

`-b^2+18b-80 != 0`
`implies -b^2+10b+8b-80!=0`
`implies -b(b-10)+8(b-10)1=0`
`implies (b-10)(-b+8)!=0`
`implies b!= 10, 8`

Hence `b` cannot be either `0` or `8` or `10`.
`therefore b !=0, 8, 10` .
`therefore b in RR-{0, 8, 10}`