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

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

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

range

f (x) = 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

3 (\frac{1}{2})^{x}

\frac{3 x ^{2} - 12 x}{x ^{2} - 2 x - 3}

\frac{x ^{2} - 3}{x - 2}

f (x) = - x^{2} + 4 x + 6

f (x) = \frac{1}{3} x^{3} - x