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Find the real values of x for which the ...

Find the real values of x for which the function `f(x) = cos^(-1) sqrt(x^(2) + 3 x + 1) + cos^(-1) sqrt(x^(2) + 3x)` is defined

Text Solution

Verified by Experts

The correct Answer is:
`x = 0, -3`
We have `f(x) = cos^(-1) sqrt(x^(2) + 3x + 1) + cos^(-1) sqrt(x^(2) + 3x)`
We must have `0 le x^(2) + 3x + 1 le 1 and 0 le x^(2) + 3x le 1`
`rArr x^(2) + 3x = 0`
`rArr x = 0, -3`
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