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Popular Calculus >

f(x)=x^{1/x}

Solution

f (x) = x^{\frac{1}{x}}

Solution

Domain : x > 0

Range : 0 < f (x) \leq e^{\frac{1}{e}}

Intercepts : None

Asymptotes : Horizontal y = 1

Extreme Points : Maximum (e, e^{\frac{1}{e}})

+1

Interval Notation

Domain : (0, \infty)

Range : (0, e^{\frac{1}{e}}]

Solution steps

Domain of

x^{\frac{1}{x}} : x > 0

Range of

x^{\frac{1}{x}} : 0 < f (x) \leq e^{\frac{1}{e}}

Axis interception points of

x^{\frac{1}{x}} :

None

Asymptotes of

x^{\frac{1}{x}} :

Horizontal

: y = 1

Extreme Points of

x^{\frac{1}{x}} :

Maximum

(e, e^{\frac{1}{e}})

Graph

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Frequently Asked Questions (FAQ)

What is the f(x)=x^{1/x} ?
The f(x)=x^{1/x} is