Question

The functions that is identical to f(x) =
$f\left(x\right)=\{\begin{array}{cc}x,& 1\le x<2\\ x^2,& 2\le x<3\end{array}$

for (1 $\le$ x < 3) is

• 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 .

For $[x{]}^x$

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

$\Rightarrow$ Wrong

functions $x^2$, $x^3$ 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 )

The function $x^{\left[x\right]}$ satisfies all the condtions

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

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