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Question

Let f(x)=log2(x26x+8). Then

A
domain of f(x) is R[2,4]
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B
domain of f(x) is (2,4)
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C
range of f(x) is R
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D
range of f(x) is R+
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Solution

The correct option is C range of f(x) is R
Given : f(x)=log2(x26x+8)=log2[(x2)(x4)]
For domain : (x2)(x4)>0
x(,2)(4,)

Let y=x26x+8=(x3)21
y>1 for x(,2)(4,)
But y should be positive.
y>0
Since logax is an increasing function for a>1,
Range is (,)

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