Let `f={(2,4),(5,6),(8,-1),(10,3)`
and `g={(2,5),(7,1),(8,4),(10,13),(11,5)}`
be two real functions. Then, match the following .

The domain of `f-g,f+g,f*g,(f)/(g)` is domain of f `nn` domain of g. Then, find their images.

Explanation

We have
`f={(2,4),(5,6),(8,1),(10,-3)`
and `g={(2,5),(7,1),(8,4),(10,13),(11,5)}`
So, `f-g,f+g,f*g,(f)/(g)` are defined in the domain (domain of f`nn` domain of g)
`i.e., {2,5,8,10}nn{2,7,8,10,11} rArr {2,8,10}`
(i) `(f-g)(2)=f(2)-g(2)=4-5=-1`
`(f-g)(8)=f(8)-g(8)=-1-4=-5`
`(f-g)(10)=f(10)-g(10)=-3-13=-16`
`f-g={(2,-1),(8,-5),(10,-16)}`
(ii) `(f+g) (2)=f(2)=f(2)+g(2)=4+5=9`
`(f+g)(8)=f(8)+g(8)=-1+4=3`
`(f+g)(10)=f(10)+g(10)=-3+13=10`
`:. f-g={(2,9).(8,3),(10,10)}`
(iii) `(f-g )(2)=f(2)*g(2)=4xx5=20`
`(f*g)(8)=f(8)*(8)=-1xx4=-4`
`(f*g)(10)=f(10)*g(10)=-3xx13=-39`
`:. fg={(2,20),(8,-4),(10,-39)}`
(iv) `((f)/(g))(2)=(f(2))/(g(2))=(4)/(5)`
`((f)/(g))(8)=(f(8))/(g(8))=(-1)/(4)`
`((f)/(g))(10)=(f(10))/(g(10))=(-3)/(13)`
`:. (f)/(g)={(2,(4)/(d)),(8,-(1)/(4)),(10,(-3)/(13))}`
Hence , the correct matches are `(i) rarr(c),(ii) rarr(d),(iii)rarr(b), (iv) rarr(a).`