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The function f: (a, oo) ->R where R deno...

The function `f: (a, oo) ->R` where R denotes the range corresponding to the given domain, with rule `f(x)=2x-3x^2 +6`, will have an inverse provided

A

`a le1`

B

`age0`

C

`ale0`

D

`age1`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=2x^(3)-3x^(2)+6`
`f'(x)=6x^(2)-6x=6(x^(2)-x)=0`
`rArr" "x=0 or x=1`

For inverse to exist function must be one onto
Hence domain is `[1,oo)`
Hence `a le 1`
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