Question

If `x in R " and "alpha=(x^(2))/(1+x^(4))`, then `alpha` lies in the interval
A. [0,2]
B. [0,1]
C. `[0,1//2]`
D. `[1//2,1]`

Answer 1

Correct Answer - C
Using `A.M.geG.M.,` we have
`(1+x^(4))/(2)gesqrt(1xxx^(4))`
`implies" "(1+x^(4))/(2)gex^(2)`
`implies" "(1+x^(4))/(x^(2))ge2implies0le(x^(2))/(1+x^(4))le(1)/(2)implies0lealphale(1)/(2)`