Question

Let f : $R-\left\{1\right\}\to R$ be defined by $f\left(x\right)=x+1$ and $g\left(x\right):R-\left\{1\right\}\to R$ be defined by $g\left(x\right):\frac{x^2-1}{x-1}$ Show that f=g.

Answer 1

$g\left(x\right)=\frac{x^2-1}{x-1}=\frac{(x-1)(x+1)}{(x-1)}=x+1$

and also $f\left(x\right)=x+1$

So, we can say that $f=g$