Range

Find the range of f(x)=ln(1+x²/1+x+x²).

is the ans [ln(2/3),ln(2)] ?

1 Answers

1+x²/1+x+x²

= 1 - x/(1+x+x²)

= 1 - 1/(1+x+1/x)

now x+1/x is never between (-2,2)

so the denominator (1+x+1/x) will be never between (-1,3)

the reciprocal will take values between [-1,1/3]

so the above expression will take value between [2/3,2]

hence ur above answer is reached bcos ln is an increasing function!

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