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Give answer! - Algebra - BITSAT

The largest inerval among the following for which y^{12}-y^{9}+y^{4}-y+1>0 is

  • Option 1)

    -4<y\leqslant 0

  • Option 2)

    0<y<1

  • Option 3)

    -100<y<100

  • Option 4)

    -\infty<y<\infty

 
Answers (1)
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As learnt in concept

Range -

The range of the relation R is the set of all second elements of the ordered pairs in a relation R.

- wherein

eg. R={(a,b),(c,d)}. Then Range is {b,d}

 

 f(y)=y^{12}-y^{9}-y^{4}-y+1>0

Case I when y<0

Then, y^{12}>0\: \ -y^{9}>0\: \ \ \ y^{4}>0\: \ \ -y>0 and thus, f(y)>0

Case II y>1

y^{12}>y^{9} and y^{4}-y>0

Thus f(y)>0

Case III: y\in (0,1)

Then 1>y and y^{4}>y^{9}

Thus f(y)>0


Option 1)

-4<y\leqslant 0

This is incorrect option

Option 2)

0<y<1

This incorrect option

Option 3)

-100<y<100

This incorrect option

Option 4)

-\infty<y<\infty

This correct option

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