What is the range of f(x)=20t-t^2 ?

The range of f(x)=20t-t^2 is f(x)<= 100

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range of f(x)=20t-t^2

range

f (x) = 20 t - t^{2}

f (x) \leq 100

Interval Notation

(- \infty, 100]

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

20 t - t^{2}

Inverse of

20 t - t^{2} : 10 - - t + 100, - t + 100 + 10

10 - - t + 100, - t + 100 + 10

Find the domain of each inverse function

Domain of

10 - - t + 100 : t \leq 100

Domain of

- t + 100 + 10 : t \leq 100

Combine the intervals

f (x) \leq 100

- 3 sin (- 2 x + \frac{π}{2})

f (x) = x + 2 - 2

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

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

g (x) = x^{3} + 1