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Popular >

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

Solution

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

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq 22

Y Intercepts : (0, 3)

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [22, \infty)

Solution steps

Domain of

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

Range of

2 e^{x} + e^{- x} : f (x) \geq 22

Axis interception points of

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

Y Intercepts

: (0, 3)

Asymptotes of

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

None

Extreme Points of

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

Minimum

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

Popular Examples

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f (x) = \frac{( x - 5 ) ( x - 12 )}{( x + 3 ) ( x - 2 ) ( x - 5 )}

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

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

y = 6 x + 35

y=(2x+3)/(2x^2+x-1)

y = \frac{2 x + 3}{2 x ^{2} + x - 1}

f (x) = - \frac{1}{6} x^{2}

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