What is the range of e^{x^2-2x-3} ?

The range of e^{x^2-2x-3} is f(x)>= 1/(e^4)

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range of e^{x^2-2x-3}

range

e^{x^{2} - 2 x - 3}

f (x) \geq \frac{1}{e ^{4}}

Interval Notation

[\frac{1}{e ^{4}}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

e^{x^{2} - 2 x - 3}

Inverse of

e^{x^{2} - 2 x - 3} : 1 + ln (x) + 4, 1 - ln (x) + 4

1 + ln (x) + 4, 1 - ln (x) + 4

Find the domain of each inverse function

Domain of

1 + ln (x) + 4 : x \geq \frac{1}{e ^{4}}

Domain of

1 - ln (x) + 4 : x \geq \frac{1}{e ^{4}}

Combine the intervals

f (x) \geq \frac{1}{e ^{4}}

f (x) = \frac{x - 13}{2}

f (x) = \frac{- 3}{x - 2}

f (x) = \frac{2}{x ^{2} - 2 x - 3}

f (x) = y

f (x) = \frac{3}{2 x - 4}