Le `f:[0,\ oo)->R\ a n d\ g: R->R` be defined by `f(x)=sqrt(x)` and `g(x)=xdot` Find `f+g,\ f-g,\ fg\ a n df/gdot`

Explanation

` (i) D(f+g)=[0, oo] cap R=[0, oo]`

`f+g[0, oo]->R` is given by `(f+g)(x)=f(x)+g(x)=sqrt(x)+x`



(ii) `D(f-g)=D(f) cap D(g)=[0, oo] cap R= [0, oo]`

`f-g: (0, oo)->R` is given by
`(f-g)(x)-g(x)=sqrt(x)-x`

`D(fg)=D(f) cap D(g)=[0, oo] cap R=[0, oo]`

(iii) `f(g):(0, oo)->R` is defined as`(fg)(x)=f(x)g(x)=sqrt(x)=x^(frac{3}{2})`

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