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Q.

Let A=[a,∞) denotes domain, then f:[a,∞)→B,f(x)=2x3−3x2+6 will have an inverse for  the smallest real value of a, if :

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a

a=1,B=[5,∞)

b

a=2,B=[10,∞)

c

a=0,B=[6,∞)

d

a=−1,B=[1,∞)

answer is A.

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Detailed Solution

f(x)=2x3−3x2+6f′(x)=6x2−6x≥0 ⇒x∈[1,∞) and f(x)∈[5,∞)
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Let A=[a,∞) denotes domain, then f:[a,∞)→B,f(x)=2x3−3x2+6 will have an inverse for  the smallest real value of a, if :