Question

The domain for which the functions $f(x)=2x^{2}-1$ and $g(x)=1-3x$ are equal, is

• A. $R$
• B. $\left\{-2, \frac{1}{2}\right\}$
• C. $R^{+}$
• D. $\left\{2, \frac{1}{2}\right\}$

Answer 1

Answer: (B)

For $ f\left(x\right) = g\left(x\right)$
$\Rightarrow 2x^{2} - 1 = 1 - 3x$
$\Rightarrow 2x^{2} + 3 x -2 = 0$
$\Rightarrow 2x^{2} + 4 x - x - 2 = 0$
$\Rightarrow \left(2x-1\right)\left(x+2\right)=0$
Thus domain for which the function $f\left(x\right)=g\left(x\right)$ is
$\left\{-2, \frac{1}{2}\right\}$.