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Popular >

f(x)=x+(e^x)/(2(e^x-2))

Solution

f (x) = x + \frac{e ^{x}}{2 ( e ^{x} - 2 )}

Solution

Domain : x < ln (2) or x > ln (2)

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

Y Intercepts : (0, - \frac{1}{2})

Asymptotes : Vertical x = ln (2)

Extreme Points : Maximum (0, - \frac{1}{2}), Minimum (2 ln (2), 2 ln (2) + 1)

+1

Interval Notation

Domain : (- \infty, ln (2)) \cup (ln (2), \infty)

Range : (- \infty, - \frac{1}{2}] \cup [2 ln (2) + 1, \infty)

Solution steps

Domain of

x + \frac{e ^{x}}{2 ( e ^{x} - 2 )} : x < ln (2) or x > ln (2)

Range of

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

Axis interception points of

x + \frac{e ^{x}}{2 ( e ^{x} - 2 )} :

Y Intercepts

: (0, - \frac{1}{2})

Asymptotes of

x + \frac{e ^{x}}{2 ( e ^{x} - 2 )} :

Vertical

: x = ln (2)

Extreme Points of

x + \frac{e ^{x}}{2 ( e ^{x} - 2 )} :

Maximum

(0, - \frac{1}{2}),

Minimum

(2 ln (2), 2 ln (2) + 1)

Graph

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Frequently Asked Questions (FAQ)

What is the f(x)=x+(e^x)/(2(e^x-2)) ?
The f(x)=x+(e^x)/(2(e^x-2)) is