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Question

Which of the following intervals belong(s) to the domain of the function f(x)=log0.4(x41)x2+2x+8


Your Answer
A
(1,)
Your Answer
B
[42,42]
Correct Answer
C
[2,)
Correct Answer
D
[32,42]

Solution

The correct options are
C [2,)
D [32,42]
(i)  x2+2x+8=(x+1)2+70  xR

(ii)  x41>0
(x2+1)(x+1)(x1)>0
x(,1)(1,)

(iii) log0.4(x41)0
log0.4(x41)0
x411
x420
(x2+2)(x+42)(x42)0
x(,42][42,)

Domain is (,42][42,)

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