Question

Which of the following functions are identical to
$f\left(x\right)=\{\begin{array}{cc}x,& 1\le x<2\\ x^2,& 2\le x<3\end{array}$

Answer 1

We will go through the options and eliminate .

(A) $[x{]}^x$

If 1 $\le x<2,\left[x\right]=1$,
$[x{]}^x=1^x=1$

$\Rightarrow$ So it is wrong.

(C), (D) are wrong because in the interval $1\le x<2$

they are not equal to $x$
but $f\left(x\right)$ is equal to $x$ in this interval .

(B) Satisfies all the condtions

$\left[x\right]=1$ , if $1\le x<2$

$\left[x\right]=2$ , if $2\le x<3$