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Popular >

y= 2/3 e^x+e^{-2x}

Solution

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

Solution

Domain : - \infty < x < \infty

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

Y Intercepts : (0, \frac{5}{3})

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

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

Solution steps

Domain of

\frac{2}{3} e^{x} + e^{- 2 x} : - \infty < x < \infty

Range of

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

Axis interception points of

\frac{2}{3} e^{x} + e^{- 2 x} :

Y Intercepts

: (0, \frac{5}{3})

Asymptotes of

\frac{2}{3} e^{x} + e^{- 2 x} :

None

Extreme Points of

\frac{2}{3} e^{x} + e^{- 2 x} :

Minimum

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

Popular Examples

y = 4^{x - 2}

f(x)=3x-5x^2+8x^4-2

f (x) = 3 x - 5 x^{2} + 8 x^{4} - 2

f (x) = - \frac{x}{2} - 7

f (x) = x^{2} + 2 x - 16

f (x) = x^{2} + 2 x - 63

Frequently Asked Questions (FAQ)

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