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The range of function f(x)=^(7-x)P(x-3)i...

The range of function `f(x)=^(7-x)P_(x-3)i s` {1,2,3} (b) `{1,2,3,4,5,6}` `{1,2,3,4}` (d) `{1,2,3,4,5}`

A

`{1,2,3}`

B

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

C

`{1,2,3,4}`

D

`{1,2,3,4,5}`

Text Solution

Verified by Experts

The correct Answer is:
A
We have `f(x)=""^(7-x)P_(x-3)=((7-x)!)/((10-2x)!)`
We must have `7-x gt 0, x ge 3, " and " 7-x ge x-3.` Therefore,
`x lt 7, x ge 3, " and " x le 5`
or ` 3 le x le 5`
or ` x =3,4,5`
Now, `f(3)=(4!)/(4!)=1, f(4)=(3!)/(2!)=3,f(5)=(2!)/(0!)=2.`
Hence, `R_(f)={1,2,3}.`
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