Question

If `R_(1)={(x,y)|y=2x+7,` where `x in R` and `-5 le x le 5}` is a relation. Then find the domain and Range of `R_(1)`.
A. `(3)/(4)`
B. `(1)/(2)`
C. `(1)/(3)`
D. `(1)/(4)`

Answer 1

Correct Answer - b
Clearly,
`R_(1)=underset(0)overset(b)int(1-x)^(2)dx and R_(2)=underset(0)overset(1)int(1-x)^(2)dx`

`implies R_(1)=[((x-1)^(3))/(3)]_(0)^(b) and , R_(2)=[((x-1)^(3))/(3)]_(b)^(1)`
`impliesR_(1)=((b-1)^(3))/(3)+(1)/(3) and , R_(2)=-((b-1)^(3))/(3)`
`therefore R_(1)-R_(2)=(1)/(4)`
`implies (2)/(3)(b-1)^(3)+(1)/(3)=(1)/(4)`
`implies (2)/(3)(b-1)^(3) =-(1)/(12)`
`implies (b-1)^(3)=-(1)/(8)impliesb-1=-(1)/(2)implies b=(1)/(2)`