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Popular >

y=5^{3x}+e^{-10x}

Solution

y = 5^{3 x} + e^{- 10 x}

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq 5^{\frac{3 ( l n ( 10 ) - l n ( 3 l n ( 5 ) ) )}{3 l n ( 5 ) + 10}} + \frac{1}{e ^{\frac{10 ( l n ( 10 ) - l n ( 3 l n ( 5 ) ) )}{3 l n ( 5 ) + 10}}}

Y Intercepts : (0, 2)

Asymptotes : None

Extreme Points : Minimum (\frac{ln ( 10 ) - ln ( 3 ln ( 5 ) )}{3 ln ( 5 ) + 10}, 5^{\frac{3 ( l n ( 10 ) - l n ( 3 l n ( 5 ) ) )}{3 l n ( 5 ) + 10}} + \frac{1}{e ^{\frac{10 ( l n ( 10 ) - l n ( 3 l n ( 5 ) ) )}{3 l n ( 5 ) + 10}}})

+1

Interval Notation

Domain : (- \infty, \infty)

Solution steps

Domain of

5^{3 x} + e^{- 10 x} : - \infty < x < \infty

Range of

5^{3 x} + e^{- 10 x} : f (x) \geq 5^{\frac{3 ( l n ( 10 ) - l n ( 3 l n ( 5 ) ) )}{3 l n ( 5 ) + 10}} + \frac{1}{e ^{\frac{10 ( l n ( 10 ) - l n ( 3 l n ( 5 ) ) )}{3 l n ( 5 ) + 10}}}

Axis interception points of

5^{3 x} + e^{- 10 x} :

Y Intercepts

: (0, 2)

Asymptotes of

5^{3 x} + e^{- 10 x} :

None

Extreme Points of

5^{3 x} + e^{- 10 x} :

Minimum

(\frac{ln ( 10 ) - ln ( 3 ln ( 5 ) )}{3 ln ( 5 ) + 10}, 5^{\frac{3 ( l n ( 10 ) - l n ( 3 l n ( 5 ) ) )}{3 l n ( 5 ) + 10}} + \frac{1}{e ^{\frac{10 ( l n ( 10 ) - l n ( 3 l n ( 5 ) ) )}{3 l n ( 5 ) + 10}}})

Graph

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Frequently Asked Questions (FAQ)

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