Question

The domain for which the functions $f\left(x\right)=2x^2-1$ and $g\left(x\right)=1-3x$ are equal is

• A. $\{1,2\}$
• B. $\{-2,2\}$
• C. $\{-2,\pm \frac{1}{\sqrt{2}}\}$
• D. $\{0,1\}$

Answer 1

The correct option is C $\{-2,\pm \frac{1}{\sqrt{2}}\}$

$f\left(x\right)=2x^2-1;g\left(x\right)=1-3x$

$2x^2-1=1-3x$

$2x^2+3x-2=0$

$2x^2+3x-2=0$

$2x^2+4x-x-2=0$

$2x^2(x+2)-1(x+2)=0$

$(2x^2-1)(x+2)=0$

$x=\frac{1}{\sqrt{2}},\frac{-1}{\sqrt{2}},-2$