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The function f:[0,3] to [1,29], defined ...

The function `f:[0,3] to [1,29],` defined by `f(x)=2x^(3)-15x^(2)+36x+1` is

A

one-one and onto

B

onto but not one-one

C

one-one but not onto

D

Neither one-one nor onto

Text Solution

Verified by Experts

The correct Answer is:
B
`f:[0,3]to[1,29]`
and `" "f(x)=2x^(3)-15x^(2)+36x+1`
`:." "f'(x)=6x^(2)-30x+36=6(x-2)(x-3)`
`("+ - +")/(2" "3)`
For given domain [0, 3], f(x) is increasing as well as decreasing.
So, it is many-one function.
Now, `" "f'(x)=0`
`implies" "x=2,3`
Thus, for range `f(0)=1,f(2)=29,f(3)=28`
`implies" ""Range "in[1,29]`
So, it is onto function.
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