Solve h= -16x^2 6x^5

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{7 9 6 ^{6} x}{96}

Evaluate

h = - 16 x^{2} \times 6 x^{5}

Simplify

More Steps

Evaluate

- 16 x^{2} \times 6 x^{5}

Multiply the terms

- 96 x^{2} \times x^{5}

Multiply the terms with the same base by adding their exponents

- 96 x^{2 + 5}

Add the numbers

- 96 x^{7}

h = - 96 x^{7}

Interchange x and y

x = - 96 y^{7}

Swap the sides of the equation

- 96 y^{7} = x

Change the signs on both sides of the equation

96 y^{7} = - x

Divide both sides

\frac{96 y ^{7}}{96} = \frac{- x}{96}

Divide the numbers

y^{7} = \frac{- x}{96}

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

y^{7} = - \frac{x}{96}

Take the 7 -th root on both sides of the equation

7 y^{7} = 7 - \frac{x}{96}

Calculate

y = 7 - \frac{x}{96}

Simplify the root

More Steps

Evaluate

7 - \frac{x}{96}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{7 - x}{7 96}

Multiply by the Conjugate

\frac{7 - x \times 7 9 6 ^{6}}{7 96 \times 7 9 6 ^{6}}

Calculate

\frac{7 - x \times 7 9 6 ^{6}}{96}

Calculate

More Steps

Evaluate

7 - x \times 7 9 6^{6}

The product of roots with the same index is equal to the root of the product

7 - x \times 9 6^{6}

Calculate the product

7 - 9 6^{6} x

An odd root of a negative radicand is always a negative

- 7 9 6^{6} x

\frac{- 7 9 6 ^{6} x}{96}

Calculate

- \frac{7 9 6 ^{6} x}{96}

y = - \frac{7 9 6 ^{6} x}{96}

Solution

f^{- 1} (x) = - \frac{7 9 6 ^{6} x}{96}

Show Solution

Solve the equation

Solve for x

Solve for h

x = - \frac{7 9 6 ^{6} h}{96}

Evaluate

h = - 16 x^{2} \times 6 x^{5}

Simplify

More Steps

Evaluate

- 16 x^{2} \times 6 x^{5}

Multiply the terms

- 96 x^{2} \times x^{5}

Multiply the terms with the same base by adding their exponents

- 96 x^{2 + 5}

Add the numbers

- 96 x^{7}

h = - 96 x^{7}

Swap the sides of the equation

- 96 x^{7} = h

Change the signs on both sides of the equation

96 x^{7} = - h

Divide both sides

\frac{96 x ^{7}}{96} = \frac{- h}{96}

Divide the numbers

x^{7} = \frac{- h}{96}

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

x^{7} = - \frac{h}{96}

Take the 7 -th root on both sides of the equation

7 x^{7} = 7 - \frac{h}{96}

Calculate

x = 7 - \frac{h}{96}

Solution

More Steps

Evaluate

7 - \frac{h}{96}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{7 - h}{7 96}

Multiply by the Conjugate

\frac{7 - h \times 7 9 6 ^{6}}{7 96 \times 7 9 6 ^{6}}

Calculate

\frac{7 - h \times 7 9 6 ^{6}}{96}

Calculate

More Steps

Evaluate

7 - h \times 7 9 6^{6}

The product of roots with the same index is equal to the root of the product

7 - h \times 9 6^{6}

Calculate the product

7 - 9 6^{6} h

An odd root of a negative radicand is always a negative

- 7 9 6^{6} h

\frac{- 7 9 6 ^{6} h}{96}

Calculate

- \frac{7 9 6 ^{6} h}{96}

x = - \frac{7 9 6 ^{6} h}{96}

Show Solution

Function

Solve the equation

Graph