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Let f : R - {2} rarr R be defined as f...

Let ` f : R - {2} rarr R` be defined as f(x) = `(x^2 - 4)/(x-2)` and `g: R rarr R` be defined by g(x) = x + 2. Find whether f = g or not.

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We have `f(x)=(x^2−4)/(x−2)`
`⇒f(x)=((x−2)(x+2))/(x−2)​`
`⇒f(x)=x+2`
But, `g(x)=x+2` for all `x in R`
Then, `f(x)` and` g(x)` have different domains
Domain of `f=R−{2}` and domain of `g=R`
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