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Question

If f(x)=3|x|x2, then which of the following is (are) CORRECT?

A
Range of f(x) is [0,)
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B
Range of f(x) is [1,)
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C
Domain of f(x) is (,12][1,)
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D
Domain of f(x) is (,12][1,)
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Solution

The correct options are
A Range of f(x) is [0,)
C Domain of f(x) is (,12][1,)
f(x)=3|x|x2 is defined when 3|x|x20

Case 1: When x<0
3xx20x12
x(,12]

Now, let f(x)=yy0
y2=4x2y2+2=4xx12x124x2y2+22y[0,)

Case 2: When x0
3xx20x1
x[1,)

Now, let f(x)=yy0
y2=2x2y2+2=2xx12x2y2+22 y[0,)

Hence, domain of f(x) is (,12][1,) and range of f(x) is [0,)

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