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

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

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

range

f (x) = e^{- x^{2}}

0 < f (x) \leq 1

Interval Notation

(0, 1]

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

e^{- x^{2}}

Inverse of

e^{- x^{2}} : - ln (x), - - ln (x)

- ln (x), - - ln (x)

Find the domain of each inverse function

Domain of

- ln (x) : 0 < x \leq 1

Domain of

- - ln (x) : 0 < x \leq 1

Combine the intervals

0 < f (x) \leq 1

- \frac{4}{x ^{3} - 9 x}

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

f (x) = 10 x - 6

(- 1, - 2), (2, 2)

(- 4, - 3), (3, 0)