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Popular Functions >

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

Solution

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

Solution

Domain : x < - 1 or - 1 < x < 1 or x > 1

Range : f (x) < 0 or f (x) \geq \frac{4 ln ^{2} ( 2 ) + 4 + 2}{4 \cdot 2 ^{\frac{4 l n ^{2} ( 2 ) + 4 - 2}{2 l n ( 2 )}}}

Y Intercepts : (0, 1)

Asymptotes : Vertical x = - 1, x = 1, Horizontal y = 0

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

+1

Interval Notation

Domain : (- \infty, - 1) \cup (- 1, 1) \cup (1, \infty)

Range : (- \infty, 0) \cup \frac{4 ln ^{2} ( 2 ) + 4 + 2}{4 2 ^{\frac{4 l n ^{2} ( 2 ) + 4 - 2}{2 l n ( 2 )}}}, \infty

Solution steps

Domain of

\frac{2 ^{x}}{1 - x ^{2}} : x < - 1 or - 1 < x < 1 or x > 1

Range of

\frac{2 ^{x}}{1 - x ^{2}} : f (x) < 0 or f (x) \geq \frac{4 ln ^{2} ( 2 ) + 4 + 2}{4 \cdot 2 ^{\frac{4 l n ^{2} ( 2 ) + 4 - 2}{2 l n ( 2 )}}}

Axis interception points of

\frac{2 ^{x}}{1 - x ^{2}} :

Y Intercepts

: (0, 1)

Asymptotes of

\frac{2 ^{x}}{1 - x ^{2}} :

Vertical

: x = - 1, x = 1,

Horizontal

: y = 0

Extreme Points of

\frac{2 ^{x}}{1 - x ^{2}} :

Minimum

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

Maximum

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

Graph

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Frequently Asked Questions (FAQ)

What is the f(x)=(2^x)/(1-x^2) ?
The f(x)=(2^x)/(1-x^2) is