What is the range of f(x)=(e^{-x})/(x^2+1) ?

The range of f(x)=(e^{-x})/(x^2+1) is f(x)>0

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range of f(x)=(e^{-x})/(x^2+1)

range

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

f (x) > 0

Interval Notation

(0, \infty)

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{e ^{- x}}{x ^{2} + 1} : - \infty < x < \infty

Extreme Points of

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

Saddle

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

Find the range for the interval

- \infty < x < \infty : 0 < f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

f (x) > 0

4 x^{4} - 37 x^{2} + 9

y = 4

y = x - 4

f (x) = - 3 csc (x)

f (x) = x - 7 + 8

What is the range of f(x)=(e^{-x})/(x^2+1) ?
The range of f(x)=(e^{-x})/(x^2+1) is f(x)>0