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Question

The range off(x)=6x+3x+6-x+3-x+2 is a subset of.....


A

[-,-2)

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B

(-2,3)

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C

(6,)

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D

[6,)

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Solution

The correct option is D

[6,)


The explanation for the correct option.

Compute the range.

Given: f(x)=6x+3x+6-x+3-x+2

Add and subtract 4

f(x)=6x+6-x-2+3x+3-x-2+2+4=6x-6-x2+3x-3-x2+6[(a-b)2=a2+b2-2ab]

We can see that f(x) is always positive. so the maximum value of f(x) is .

Now, find minimum value of f(x),

f(x)min=0+0+6=6

Thus, the range of the function f(x) is [6,).

Hence, option(D) is the correct answer.


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