First slide

Permutations

Question

The range of the function $f (x) =^{7 - x} P_{x - 3}$ is

Moderate

A

{1,2,3}
B

{1,2,3,4,5,6}
C

{1, 2, 3, 4}
D

{1, 2, 3, 4, 5}

Solution

We have $f (x) =^{7 - x} P_{x - 3} = \frac{(7 - x)!}{(10 - 2 x)!}$
We must have $7 - x > 0, x \geq 3, and 7 - x \geq x - 3 .$ Therefore,
$\begin{array}{l} x < 7, x \geq 3, and x \leq 5 \\ or 3 \leq x \leq 5 \\ or x = 3, 4, 5 \end{array}$
$\begin{array}{l} Now, f (3) = \frac{4!}{4!} = 1, f (4) = \frac{3!}{2!} = 3, f (5) = \frac{2!}{0!} = 2 . \\ Hence, R_{f} = \{1, 2, 3\} . \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App