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Question

The domain of the function f(x)=4x+1x21 is

A
x(,1](1,4]
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B
x(,1)(1,4]
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C
x(,1)[1,4]
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D
x(,1][1,4]
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Solution

The correct option is B x(,1)(1,4]
f(x)=4x+1x21

For domain of the given function
both (4x)0
and
(x21)>0

(4x)0
x4

and

x21>0
(x1)(x+1)>0
x<1 or x>1

on combining both conditions and finding the combined other regions, we get
x(,1)(1,4]

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