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Let f:[-1,3]-> [-8, 72] be defined as,f...

Let `f:[-1,3]-> [-8, 72]` be defined as,`f(x) = 4x^3-12x`,then f is

A

injective but not surjective

B

bijective

C

neither injective not surjective

D

surjective but not injective

Text Solution

Verified by Experts

The correct Answer is:
D
`becausef(x)=4x^(3)-12x,x in [-1,3]`
`becausef'(x)=12x^(2)-12=12(x-1)(x+1)`
`becausef(x)` is neither S.I. nor S.D. `therefore` many-one
`f'(x)=0impliesx= +-1`
`becausef(`)=-8,f(-1)=8,f(3)=108-36=72`
`therefore` Range `=[-8,72]=` condomain
`therefore` surjective
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