The range of the function `f(x)=\ ^(7-x)P_(x-3)` is (a) {1, 2, 3, 4, 5} (b) {1, 2, 3, 4, 5, 6} (c) {1, 2, 3, 4} (d) {1, 2, 3}

Options

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

Answer

D

Explanation

Clearly `f(x)=^(7-x)P_(x-3),is` defined for positive integer values of x satisfying
`7-x gt 0, x-3 ge 0 and x-3 le 7-x`
`i.e. x lt 7, x ge 3 and x-3 le 7 -x`
i.e. x=3,4,5
`therefore "Domain(f)"=(3,4,5)`
Hence, range(f)=`(f(3),f(4),F(5)={.^(4)P_(0),^(3)P_(1),^(2)P_(2)}`
={1,2,3}