1.

Let h(x) =f(x)-a(f(x))^(3) for every real number x h(x) increase as f(x) increses for all real values of x if

Answer»

`a in (0,3)`
`a in (-2,2)`
`[3,oo)`
none of these

Solution :`HH(X) =-F(X)=af(x)^(2)+a(f(x))^(3)`
or `h(X)=f(x)-2af(x)f(x)+3a(f(x))^(2)f(x)`
`=f(x)[3a(f(x))^(2)-2af(x)+1]`
Now h(x) increase if f(x) increase and
`3a(f(x))^(2)-2af(x)+1gt0for all x in R`
or `3agt0 and 4A^(2)-12ale0`
or `AGT0 and a in [0,3]`
or `a in [0,3]`


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