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}`

Options

A. `{1,2,3}`
B. `{1,2,3,4,5,6}`
C. `{1,2,3,4}`
D. `{1,2,3,4,5}`

Answer

A

Explanation

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}.`