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Popular >

f(x)=-(x+1)/2+ln(x/(x+1))

Solution

f (x) = - \frac{x + 1}{2} + ln (\frac{x}{x + 1})

Solution

Domain : x < - 1 or x > 0

Range : f (x) \leq - 1 - ln (2) or f (x) \geq \frac{1}{2} + ln (2)

Intercepts : None

Asymptotes : Vertical x = - 1, x = 0, Slant y = - \frac{1}{2} x - \frac{1}{2}

Extreme Points : Minimum (- 2, \frac{1}{2} + ln (2)), Maximum (1, - 1 - ln (2))

+1

Solution steps

Domain of

- \frac{x + 1}{2} + ln (\frac{x}{x + 1}) : x < - 1 or x > 0

Range of

- \frac{x + 1}{2} + ln (\frac{x}{x + 1}) : f (x) \leq - 1 - ln (2) or f (x) \geq \frac{1}{2} + ln (2)

Axis interception points of

- \frac{x + 1}{2} + ln (\frac{x}{x + 1}) :

None

Asymptotes of

- \frac{x + 1}{2} + ln (\frac{x}{x + 1}) :

Vertical

: x = - 1, x = 0,

Slant

: y = - \frac{1}{2} x - \frac{1}{2}

Extreme Points of

- \frac{x + 1}{2} + ln (\frac{x}{x + 1}) :

Minimum

(- 2, \frac{1}{2} + ln (2)),

Maximum

(1, - 1 - ln (2))

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Frequently Asked Questions (FAQ)

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