Question

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

(1 $\le$ x < 3)

• A. $[x{]}^x$
• B. $x^{\left[x\right]}$
• C. $x^2$
• D. $x^3$

Answer 1

The correct option is B

$x^{\left[x\right]}$

We will go through the options and eliminate .

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

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

$\Rightarrow$ Wrong

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

they are not equal to x (f(x) is equal to x in this interval )

(B) Satisfies all the condtions

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

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