Question

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

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

Answer 1

The correct option is B

$\left\{\frac{1}{2},-2\right\}$

Explanation for the correct option:

The values of $x$ for which $f\left(x\right)\text{and}g\left(x\right)$ are equal are given by:

$f\left(x\right)=g\left(x\right)$

Therefore, equating the given functions we have,

$$\begin{gathered} \Rightarrow 2x^2-1=1-3x \\ \Rightarrow 2x^2+3x-2=0 \\ \Rightarrow (x+2)(2x-1)=0 \\ \therefore x=\frac{1}{2}\mathrm{or}-2 \end{gathered}$$

Thus the value of $x$, obtained is $\left\{\frac{1}{2},-2\right\}$.

Hence, the correct answer is option (B)