Question

$f\left(x\right)=\{\begin{array}{c}0x<1\\ 2x-2x\ge 1\end{array}$, then the number of solution(s) to the equation $f\left(x\right)=x$ is:

• A. $2$
• B. $1$
• C. $4$
• D. $0$

Answer 1

The correct option is A $2$

From the given expression, we get
$f\left(0\right)=0$, since for $x<1,$ $f\left(x\right)=0$ ... $\left(i\right)$
Now $2x-2=x$
$\Rightarrow x=2$
$\Rightarrow f\left(2\right)=2,$ since for $x\ge 1,$ $f\left(x\right)=2x-2$ ... $\left(ii\right)$
Thus from $\left(i\right)$ and $\left(ii\right),$ we get
$2$ solutions for the equation $f\left(x\right)=x$