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Question

Range of the function f(x)=x2+x+2x2+x+1;x ϵ R is

A
(1,)
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B
(1,117]
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C
(1,73]
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D
[1,75]
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Solution

The correct option is C (1,73]
We have, f(x)=x2+x+2x2+x+1=(x2+x+1)+1x2+x+1=1+1(x+12)2+34
We can see here that as x,f(x)1, which is the min value of f(x). Also f(x) is max when (x+12)2+34 is min which is so when x=12 and then 34.
fmax=1+134=73
Ri=(1,73]

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