What is the f(x)=ln(e^x+xe^x) ?

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f(x)=ln(e^x+xe^x)

f (x) = ln (e^{x} + x e^{x})

Domain : x > - 1

Range : - \infty < f (x) < \infty

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

Asymptotes : Vertical x = - 1

Extreme Points : None

Interval Notation

Domain : (- 1, \infty)

Range : (- \infty, \infty)

Solution steps

Domain of

ln (e^{x} + x e^{x}) : x > - 1

Range of

ln (e^{x} + x e^{x}) : - \infty < f (x) < \infty

Axis interception points of

ln (e^{x} + x e^{x}) :

X Intercepts

: (0, 0),

Y Intercepts

: (0, 0)

Asymptotes of

ln (e^{x} + x e^{x}) :

Vertical

: x = - 1

Extreme Points of

ln (e^{x} + x e^{x}) :

None

x \to 0 lim (\frac{x ^{2} - 1}{x - 1})

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