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Let f, g : R -> R be defined, respective...

Let f, g : R `->` R be defined, respectively by `f(x)=x+1` ,`g(x)=2x-3` . Find `f+g, f-g` and `f/g` .

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(i) `(f+g)(x)=f(x)+g(x)=(x+1)+(2x-3)=3x-2`
`=3x-2`

(ii) `(f-g)(x)=f(x)-g(x)=(x+1)-(2x-3)=-x+4`
`=-x+4`

(iii) `(frac{f}{g})(x)=frac{f(x)}{g(x)}` and `g(x)!=0, x in R`
`=frac{x+1}{2x-3}, 2x-3!=0` or `x!=frac{3}{2}`
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