What is the range of f(x)= 7/2 e^{-2x^2} ?

The range of f(x)= 7/2 e^{-2x^2} is 0<f(x)<= 7/2

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range of f(x)= 7/2 e^{-2x^2}

range

f (x) = \frac{7}{2} e^{- 2 x^{2}}

0 < f (x) \leq \frac{7}{2}

Interval Notation

(0, \frac{7}{2}]

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{7}{2} e^{- 2 x^{2}}

Inverse of

\frac{7}{2} e^{- 2 x^{2}} : - \frac{ln ( \frac{2 x}{7} )}{2}, - - \frac{ln ( \frac{2 x}{7} )}{2}

- \frac{ln ( \frac{2 x}{7} )}{2}, - - \frac{ln ( \frac{2 x}{7} )}{2}

Find the domain of each inverse function

Domain of

- \frac{ln ( \frac{2 x}{7} )}{2} : 0 < x \leq \frac{7}{2}

Domain of

- - \frac{ln ( \frac{2 x}{7} )}{2} : 0 < x \leq \frac{7}{2}

Combine the intervals

0 < f (x) \leq \frac{7}{2}

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

g (t) = \frac{t - 5}{t ^{2} + 25}

(5.9, - 2.6), (2.6, - 5.9)

\frac{3}{4} (x^{2} - 1)^{\frac{2}{3}}

(2, - 1), (- 4, - 3)

What is the range of f(x)= 7/2 e^{-2x^2} ?
The range of f(x)= 7/2 e^{-2x^2} is 0<f(x)<= 7/2