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The function f(x) = cot^(-1) sqrt(x(x+3)...

The function `f(x) = cot^(-1) sqrt(x(x+3)) + cos^(-1) sqrt(x^(2) + 3x +1)` is defined on the set S, where S is equal to

A

`{-3,0}`

B

`[-3, 0]`

C

`[0, 3]`

D

`phi`

Text Solution

Verified by Experts

The correct Answer is:
A
We know that `cot^(-10 x` is defined for all `x in R` and `cos^(-1) x ` is defined for all `in [-1,1]` , Therefore,f(x) is defined if
`x(x + 3) ge 0` and `0 le x^(2)+ 3x + 1 le1`
`rArr x^(2) + 3x ge 0 and -1le x^(2) + 3x le 0 rArr x = - 3,0`
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OBJECTIVE RD SHARMA ENGLISH-REAL FUNCTIONS -Section I - Solved Mcqs
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