What is the f(x)=e^{-x}-e^{-x}x ?

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

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

Domain : - \infty < x < \infty

Range : f (x) \geq - \frac{1}{e ^{2}}

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

Asymptotes : Horizontal y = 0

Extreme Points : Minimum (2, - \frac{1}{e ^{2}})

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{e ^{2}}, \infty)

Solution steps

Domain of

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

Range of

e^{- x} - e^{- x} x : f (x) \geq - \frac{1}{e ^{2}}

Axis interception points of

e^{- x} - e^{- x} x :

X Intercepts

: (1, 0),

Y Intercepts

: (0, 1)

Asymptotes of

e^{- x} - e^{- x} x :

Horizontal

: y = 0

Extreme Points of

e^{- x} - e^{- x} x :

Minimum

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

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