Question

Find the domain for which the function $f\left(x\right)=2x^2-1$ and $g\left(x\right)=1-3x$ are equal?

Answer 1

Given, the functions $f\left(x\right)=2x^2-1g\left(x\right)=1-3x$

and, $f\left(x\right)=g\left(x\right)\Rightarrow 2x^2-1=1-3x\Rightarrow 2x^2+3x-2=0\Rightarrow 2x^2+4x-x-2=0\Rightarrow 2x(x+2)-1(x+2)=0\Rightarrow (2x-1)(x+2)=0\Rightarrow x=-2,\frac{1}{2}$

$\therefore x=-2,\frac{1}{2}$ are the two domains of for which $f\left(x\right)$ and $g\left(x\right)$ are equal.