Domain of the function, `f(x)=[log_10 ((5x-x^2)/4)]^(1/2)` is

Options

A. `-oo lt x lt oo`
B. `1 le x le 4 `
C. `4 le x le 16`
D. ` -1 le x le 1`

Answer

B

Explanation

We have `f(x)=[log_(10)((5x-x^(2))/(4))]^(1//2) " (1)" `
From (1), clearly, `f(x)` is defined for those values of `x` for which
`log_(10)[(5x-x^(2))/(4)] ge 0`
or `((5x-x^(2))/(4)) ge 10^(0)`
or `((5x-x^(2))/(4)) ge 1`
or `x^(2)-5x+4 le 0`
or `(x-1)(x-4) le 0`
Hence, the domain of the function is [1, 4].