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Let f:RtoR:f(x)=x+2andg:R-|2|toR:g(x)=(x...

Let `f:RtoR:f(x)=x+2andg:R-|2|toR:g(x)=(x^(2)-4)/(x-2)`
Show that `fne""g`. Re-define f and g such that f=g.

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We have, dom (f)= R and dom (g) `=R-{2}`
Since dom `(f)ne` dom (g), so we have `fne""g`.
For every real number `xne2`, we have
`g(x)=(x^(2)-4)/(x-2)=((x-2)(x+2))/((x-2))=(x+2)" "[:'(x-2)ne0]`.
Thus, `f(x)=g(x) "for all "x""inR-{2}`.
`:.` f=g only when, they are re-defined as under:
`f:R-|2|toR:f(x)=x+2andg:R-|2|toR:g(x)=(x^(2)-4)/(x-2)`.
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