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Popular >

f(x)=x^22^x-2^x

Solution

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

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq \frac{2 ^{\frac{- 2 + 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}} ( 2 + ln ^{2} ( 2 ) - 4 ln ^{2} ( 2 ) + 4 )}{ln ^{2} ( 2 )} - 2^{\frac{- 2 + 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}}

X Intercepts : (- 1, 0), (1, 0), Y Intercepts : (0, - 1)

Asymptotes : Horizontal y = 0

Extreme Points : Maximum \frac{- 2 - 4 + 4 ln ^{2} ( 2 )}{2 ln ( 2 )}, \frac{2 ^{\frac{- 2 - 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}} ( 2 + 4 ln ^{2} ( 2 ) + 4 + ln ^{2} ( 2 ) )}{ln ^{2} ( 2 )} - 2^{\frac{- 2 - 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}}, Minimum \frac{- 2 + 4 + 4 ln ^{2} ( 2 )}{2 ln ( 2 )}, \frac{2 ^{\frac{- 2 + 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}} ( 2 + ln ^{2} ( 2 ) - 4 ln ^{2} ( 2 ) + 4 )}{ln ^{2} ( 2 )} - 2^{\frac{- 2 + 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : \frac{2 ^{\frac{- 2 + 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}} ( 2 + ln ^{2} ( 2 ) - 4 ln ^{2} ( 2 ) + 4 )}{ln ^{2} ( 2 )} - 2^{\frac{- 2 + 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}}, \infty

Solution steps

Domain of

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

Range of

x^{2} 2^{x} - 2^{x} : f (x) \geq \frac{2 ^{\frac{- 2 + 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}} ( 2 + ln ^{2} ( 2 ) - 4 ln ^{2} ( 2 ) + 4 )}{ln ^{2} ( 2 )} - 2^{\frac{- 2 + 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}}

Axis interception points of

x^{2} 2^{x} - 2^{x} :

X Intercepts

: (- 1, 0), (1, 0),

Y Intercepts

: (0, - 1)

Asymptotes of

x^{2} 2^{x} - 2^{x} :

Horizontal

: y = 0

Extreme Points of

x^{2} 2^{x} - 2^{x} :

Maximum

\frac{- 2 - 4 + 4 ln ^{2} ( 2 )}{2 ln ( 2 )}, \frac{2 ^{\frac{- 2 - 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}} ( 2 + 4 ln ^{2} ( 2 ) + 4 + ln ^{2} ( 2 ) )}{ln ^{2} ( 2 )} - 2^{\frac{- 2 - 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}},

Minimum

\frac{- 2 + 4 + 4 ln ^{2} ( 2 )}{2 ln ( 2 )}, \frac{2 ^{\frac{- 2 + 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}} ( 2 + ln ^{2} ( 2 ) - 4 ln ^{2} ( 2 ) + 4 )}{ln ^{2} ( 2 )} - 2^{\frac{- 2 + 4 + 4 l n ^{2} ( 2 )}{2 l n ( 2 )}}

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Frequently Asked Questions (FAQ)

What is the f(x)=x^22^x-2^x ?
The f(x)=x^22^x-2^x is