Question

Examine whether following pair of functions are identical or not?
(i) `f(x)=(x^(2)-1)/(x-1)` and `g(x)=x+1`
(ii) `f(x)=sin^(2)x+cos^(2)x` and `g(x)=sec^(2)x-tan^(2)x`

Answer 1

(i) No, as domain of `f(x)` is `R-{1}`
while domain of `g(x)` is `R`
(ii) No, as domain are not same. Domain of `f(x)` is `R`
while that of `g(x)` is `R-{(2n+1)(pi)/2,n epsilonI}`