Solve h(t)=-16t^2 128t

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

h^{- 1} (t) = - \frac{3 2 t}{16}

Evaluate

h (t) = - 16 t^{2} \times 128 t

Simplify

More Steps

h (t) = - 2048 t^{3}

In the equation for h (t),replace h (t) with y

y = - 2048 t^{3}

Interchange t and y

t = - 2048 y^{3}

Swap the sides of the equation

- 2048 y^{3} = t

Change the signs on both sides of the equation

2048 y^{3} = - t

Divide both sides

\frac{2048 y ^{3}}{2048} = \frac{- t}{2048}

Divide the numbers

y^{3} = \frac{- t}{2048}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y^{3} = - \frac{t}{2048}

Take the 3 -th root on both sides of the equation

3 y^{3} = 3 - \frac{t}{2048}

Calculate

y = 3 - \frac{t}{2048}

Simplify the root

More Steps

y = - \frac{3 2 t}{16}

Solution

h^{- 1} (t) = - \frac{3 2 t}{16}

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