What is the range of f(x)=e^{x^2-6x+8} ?

The range of f(x)=e^{x^2-6x+8} is f(x)>= 1/e

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range of f(x)=e^{x^2-6x+8}

range

f (x) = e^{x^{2} - 6 x + 8}

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

Interval Notation

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

e^{x^{2} - 6 x + 8}

Inverse of

e^{x^{2} - 6 x + 8} : 3 + ln (x) + 1, 3 - ln (x) + 1

3 + ln (x) + 1, 3 - ln (x) + 1

Find the domain of each inverse function

Domain of

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

Domain of

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

Combine the intervals

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

What is the range of f(x)=e^{x^2-6x+8} ?
The range of f(x)=e^{x^2-6x+8} is f(x)>= 1/e