What is the range of f(x)=3-t^2 ?

The range of f(x)=3-t^2 is f(x)<= 3

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range of f(x)=3-t^2

range

f (x) = 3 - t^{2}

f (x) \leq 3

Interval Notation

(- \infty, 3]

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

3 - t^{2}

Inverse of

3 - t^{2} : - t + 3, - - t + 3

- t + 3, - - t + 3

Find the domain of each inverse function

Domain of

- t + 3 : t \leq 3

Domain of

- - t + 3 : t \leq 3

Combine the intervals

f (x) \leq 3

f (x) = x^{2} - 4 x + 1

f (x) = 2 x e^{- 5 x}

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

\frac{1}{x}

f (x) = (\frac{1}{2})^{x}