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Question

Let f:R[0.π2) be defined by f(x)=tan1(x2+x+a). Then the set of values of a for which f is onto is

A
[0,)
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B
[14,)
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C
(,14]
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D
{14}
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Solution

The correct option is B [14,)

We know for a function to be an onto function, Range should be equal to co-domain.
Here co-domain which is given is - [0.π2)
To have the range [0.π2) domain should have all non zero values.
x2+x+a0
this quadratic will be non zero if its discriminant is less than and equal to zero, Since it has coefficient of x2 positive.
Discriminant 14a0
a14

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