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If x is any real number, then (x^(2))/(1...

If x is any real number, then `(x^(2))/(1+x^(4))` belongs to which one of the following intervals?

A

(0,1)

B

`(0,(1)/(2)]`

C

`(0,(1)/(2))`

D

[0,1]

Text Solution

Verified by Experts

The correct Answer is:
B
`y=(x^(2))/(1+x^(4))impliesyge0`.
Also, `y=(x^(2))/(1+4^(2))=(1)/(x^(2)+(1)/(x^(2)))`
`impliesyle(1)/(2)`.
`:.(x^(2))/(1+x^(4))" belongs to "(0,(1)/(2)]`.
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