What is the range of e^{x^2} ?

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

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range of e^{x^2}

range

e^{x^{2}}

f (x) \geq 1

Interval Notation

[1, \infty)

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) : x \geq 1

Domain of

- ln (x) : x \geq 1

Combine the intervals

f (x) \geq 1

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

y = \frac{x}{x ^{2} + 1}

f (x) = - x + 2

f (x) = 2^{3 - x} - 7

f (x) = \frac{\frac{x}{1 + x}}{1 + \frac{x}{1 + x}}