If `A={-2,-1,0,1,2}` and `f : A->B` is an onto function defined by `f(x)=x^2+x+1` and find `B`.

Answer

`ararrp;s;brarrp,s;crarrq,r;d;drarrq`

Explanation

f(x)=`x^(2)logx`
For `f(X) =x(2 logx +1)=0 x=(1)/sqrt(e )` which is the point of minima as derivative change sign form negative to positive
Also the function decreases in `0,(1)/sqrt(e )`
(b) y=x logx
`therefore (dy)/(dx)=xxx1/x+logxxx1`
`=1+logx and (d^(2)y)/(dx^(2))=1/x`
for `(dy)/(dx)=0 logx =-1 or x =1/x`
`(d^(2)y)/(dx^(2))=(1)/(1//e) =egt0 at x=1/e`
Thus y is minimum for `x =1/e`
Thus y is minimum for `x =1/e`
(c ) `f(X) =(logx)/(x)`
For `f(x) =(1-logx)/(x^(2)) =0 x=e` Also derevative changes singn form positive to negative at x =e hence it is the point of maxima
(d) `f(X)=x^(-x)`
`f(x) =-x^(-x)(1+logx)=0 or x=1//e`
Which is clearly point of maxima