Question

The range of the function $f\left(x\right)={}^{5-x}P_{x-1}$.

• A. $\{1,2\}$
• B. $\{1,2,3\}$
• C. $\{1,2,3,4,5\}$
• D. $\left\{1\right\}$

Answer 1

The correct option is B

$\{1,2,3\}$

Explanation for the correct option:

Find the range of the given function

Given, $f\left(x\right)={}^{5-x}P_{x-1}$

The permutation is the arrangement of the object in a specific order.

Now, $f\left(x\right)$ is defined when,

$\left(5-x\right)>0$, $\left(x-1\right)\ge 0$ and $\left(5-x\right)\ge \left(x-1\right)$

So, $x<5,x\ge 1$ and $x\le 3$

Now, $x=1,2,3$

Range of $f\left(x\right)=\left\{f\left(1\right),f\left(2\right),f\left(3\right)\right\}$

$$\begin{gathered} =\left\{{}^{4}P_0,{}^{3}P_1,{}^{2}P_2\right\} \\ =\left\{1,3,2\right\} \end{gathered}$$

Hence, the correct option is $B$.