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Which of the following functions is/are ...

Which of the following functions is/are bounded?

A

`f(x)=(2x)/(1+x^(2)),[-2,2]`

B

`f(x)=(x^(2))/(1-x),x in [0,2]-[1]`

C

`f(x)=(x^(3)-8x+6)/(4x+1),[0,5]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, C
`f(x)=(2x)/(1+x^(2)),[-2,2]" has range "[-1,1]," hence bounded."`
`f(x)=(x^(2))/(1-x),x in [0,2]-{1}" is unbounded as"f(x)rarroo," when "xrarr1^(-)`
`f(x)=(x^(3)-8x+6)/(4x+1),[0,5]" is bounded because domain does not contain"-1//4.`
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