Question

If $f\left(x\right)=sgn\left(x\right)$ and $g\left(x\right)=x(x^2-7x+12)$, then the number of points of discontinuity of $f\left(g\right(x\left)\right)$ is

• A. $3$
• B. $2$
• C. $4$
• D. $1$

Answer 1

The correct option is A $3$

$f\left(x\right)=sgn\left(x\right)g\left(x\right)=x(x-4)(x-3)$

$f\left(g\right(x\left)\right)=sgn\left(x\right(x-4\left)\right(x-3\left)\right)$

$\Rightarrow 3$ point $0,4,3$