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Popular >

f(x)=(e^{1/x})/(x-2)

Solution

f (x) = \frac{e ^{\frac{1}{x}}}{x - 2}

Solution

Domain : x < 0 or 0 < x < 2 or x > 2

Range : f (x) \leq - e or - \frac{1}{4 e ^{\frac{1}{2}}} \leq f (x) < 0 or f (x) > 0

Intercepts : None

Asymptotes : Vertical x = 0, x = 2, Horizontal y = 0

Extreme Points : Minimum (- 2, - \frac{1}{4 e ^{\frac{1}{2}}}), Maximum (1, - e)

+1

Interval Notation

Domain : (- \infty, 0) \cup (0, 2) \cup (2, \infty)

Range : (- \infty, - e] \cup [- \frac{1}{4 e ^{\frac{1}{2}}}, 0) \cup (0, \infty)

Solution steps

Domain of

\frac{e ^{\frac{1}{x}}}{x - 2} : x < 0 or 0 < x < 2 or x > 2

Range of

\frac{e ^{\frac{1}{x}}}{x - 2} : f (x) \leq - e or - \frac{1}{4 e ^{\frac{1}{2}}} \leq f (x) < 0 or f (x) > 0

Axis interception points of

\frac{e ^{\frac{1}{x}}}{x - 2} :

None

Asymptotes of

\frac{e ^{\frac{1}{x}}}{x - 2} :

Vertical

: x = 0, x = 2,

Horizontal

: y = 0

Extreme Points of

\frac{e ^{\frac{1}{x}}}{x - 2} :

Minimum

(- 2, - \frac{1}{4 e ^{\frac{1}{2}}}),

Maximum

(1, - e)

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Frequently Asked Questions (FAQ)

What is the f(x)=(e^{1/x})/(x-2) ?
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