The domain of the function f(x)=√0.6254−3x−1.6x(x+8) is
A
(−1,4)
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B
[−1,4]
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C
[−4,−1]
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D
(−4,−1)
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Solution
The correct option is C[−4,−1] f(x)=√0.6254−3x−1.6x(x+8) For f(x) to be defined 0.6254−3x−1.6x(x+8)≥0 ⇒0.6254−3x≥1.6x(x+8)⇒(58)4−3x≥(85)x(x+8)⇒(85)3x−4≥(85)x(x+8)⇒3x−4≥x2+8x⇒x2+5x+4≤0⇒(x+4)(x+1)≤0∴x∈[−4,−1]