Question

If $f\left(x\right)=x^2-1,g\left(x\right)=(x-1{)}^{-1}$, and $x\ne 1$, then simplify $f\left(x\right)g\left(x\right)$.

• A. $2x+1$
• B. $x+1$
• C. $x-1$
• D. $x^3-1$
• E. $2x-1$

Answer 1

The correct option is B $x+1$

Given, $f\left(x\right)=x^2-1,g\left(x\right)=(x-1{)}^{-1}$

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