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The function f:(-oo,-1)vec(0, e^5) defin...

The function `f:(-oo,-1)vec(0, e^5)` defined by `f(x)=e^x^(3-3x+2)` is many one and onto many one and into one-one and onto one-one and into

A

one-one and into

B

one-one and into

C

many-one and into

D

many-one and onto

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`f(x)=e^(x^(3)3x+2)`
`Rightarrow f'(x)=3e^(x^(3)-3x+2)(x^(2)-1) ge0" for all" x in (-oo,-1)`
`Rightarrow f(x)"is strictly increasing on "(-oo,-1)`
`Rightarrow` f is one-one on `(-oo,-1]`
`Rightarrow " Range of f"=(f(-oo),f(-1)]=(0,e^(4)) ne(0,e^(5)]`
Hence, f is one-one and into functions.
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