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Popular >

f(x)=3^{x/(x^2+2x+2)}

Solution

f (x) = 3^{\frac{x}{x ^{2} + 2 x + 2}}

Solution

Domain : - \infty < x < \infty

Range : e^{- \frac{l n ( 3 )}{2} - \frac{l n ( 3 )}{2}} \leq f (x) < 1 or 1 < f (x) \leq e^{\frac{l n ( 3 )}{2} - \frac{l n ( 3 )}{2}}

Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Minimum - 2, \frac{1}{3 ^{\frac{1}{2 ^{\frac{1}{2}} ( 2 - 2 )}}}, Maximum (2, 3^{\frac{1}{2 ^{\frac{1}{2}} ( 2 + 2 )}})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [e^{- \frac{l n ( 3 )}{2} - \frac{l n ( 3 )}{2}}, 1) \cup (1, e^{\frac{l n ( 3 )}{2} - \frac{l n ( 3 )}{2}}]

Solution steps

Domain of

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

Range of

3^{\frac{x}{x ^{2} + 2 x + 2}} : e^{- \frac{l n ( 3 )}{2} - \frac{l n ( 3 )}{2}} \leq f (x) < 1 or 1 < f (x) \leq e^{\frac{l n ( 3 )}{2} - \frac{l n ( 3 )}{2}}

Axis interception points of

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

Y Intercepts

: (0, 1)

Asymptotes of

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

None

Extreme Points of

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

Minimum

- 2, \frac{1}{3 ^{\frac{1}{2 ^{\frac{1}{2}} ( 2 - 2 )}}},

Maximum

(2, 3^{\frac{1}{2 ^{\frac{1}{2}} ( 2 + 2 )}})

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Frequently Asked Questions (FAQ)

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