Saved Bookmarks
| 1. |
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. |
|
Answer» 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).` |
|