The range of the function `f(x) = tan sqrt((pi^(2))/(9)-x^(2))`, is

Options

A. `[0,3]`
B. `[0,sqrt(3)]`
C. `(-oo,oo)`
D. None of these

Answer

B

Explanation

Given, `f(x)=tansqrt((pi^(2))/(9)-x^(2))`
For f(x) to be defined, `(pi^(2))/(9)-x^(2)ge0`
`implies" "x^(2)le(pi^(2))/(9)implies-(pi)/(3)lexle(pi)/(3)`
`:." Domain of "f=[-(pi)/(3),(pi)/(3)]`
Since, the greatest value of f(x) is `tansqrt((pi^(2))/(9)-0)`, when
x = 0 and the least value of f(x) is `tansqrt((pi^(2))/(9)-(pi^(2))/(9))`, when `x=(pi)/(3)`.
So, the greatest value of f(x) is `sqrt(3)` and the least value of f(x) is 0.
`:." ""Range of "f=[0, sqrt(3)]`