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Popular >

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

Solution

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

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq \frac{1}{e ^{\frac{2 l n ( 2 )}{3}}} + e^{\frac{l n ( 2 )}{3}}

Y Intercepts : (0, 2)

Asymptotes : None

Extreme Points : Minimum (- \frac{ln ( 2 )}{3}, \frac{1}{e ^{\frac{2 l n ( 2 )}{3}}} + e^{\frac{l n ( 2 )}{3}})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{1}{e ^{\frac{2 l n ( 2 )}{3}}} + e^{\frac{l n ( 2 )}{3}}, \infty)

Solution steps

Domain of

e^{2 x} + e^{- x} : - \infty < x < \infty

Range of

e^{2 x} + e^{- x} : f (x) \geq \frac{1}{e ^{\frac{2 l n ( 2 )}{3}}} + e^{\frac{l n ( 2 )}{3}}

Axis interception points of

e^{2 x} + e^{- x} :

Y Intercepts

: (0, 2)

Asymptotes of

e^{2 x} + e^{- x} :

None

Extreme Points of

e^{2 x} + e^{- x} :

Minimum

(- \frac{ln ( 2 )}{3}, \frac{1}{e ^{\frac{2 l n ( 2 )}{3}}} + e^{\frac{l n ( 2 )}{3}})

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Frequently Asked Questions (FAQ)

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