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Let h(x) =f(x)-a(f(x))^(3) for every rea...

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

A

`a in (0,3)`

B

`a in (-2,2)`

C

`[3,oo)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
1
`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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