Question

The functions $f$ and $g$, defined by $f\left(x\right)=8x^2-2$ and $g\left(x\right)=-8x^2+2$, are graphed in the $xy$-plane above. The graphs of $f$ and $g$ intersect at the points $(k,0)$ and $(-k,0)$. What is the value of $k$ ?

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $1$
• D. $2$

Answer 1

The correct option is B $\frac{1}{2}$

Since, the graph intersect,
$\Rightarrow 8x^2-2=-8x^2+2$
$\Rightarrow 16x^2=4$
$\Rightarrow x^2=\frac{1}{4}$
$\Rightarrow x=\pm \frac{1}{2}$
Hence, $k=\frac{1}{2}$
Option B is correct.