What is the range of f(x)=e^{t^2}-4 ?

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

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range of f(x)=e^{t^2}-4

range

f (x) = e^{t^{2}} - 4

f (x) \geq - 3

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

e^{t^{2}} - 4

Inverse of

e^{t^{2}} - 4 : ln (t + 4), - ln (t + 4)

ln (t + 4), - ln (t + 4)

Find the domain of each inverse function

Domain of

ln (t + 4) : t \geq - 3

Domain of

- ln (t + 4) : t \geq - 3

Combine the intervals

f (x) \geq - 3

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

(0, 0), (8, 6)

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

x + 2 y = - 1

f (x) = \frac{4}{9} x^{2} - 6 x + 5, x = 9