Solve y = -2x^3 - 8

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 4 x + 32}{2}

Evaluate

y = - 2 x^{3} - 8

Interchange x and y

x = - 2 y^{3} - 8

Swap the sides of the equation

- 2 y^{3} - 8 = x

Move the constant to the right-hand side and change its sign

- 2 y^{3} = x + 8

Change the signs on both sides of the equation

2 y^{3} = - x - 8

Divide both sides

\frac{2 y ^{3}}{2} = \frac{- x - 8}{2}

Divide the numbers

y^{3} = \frac{- x - 8}{2}

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

y^{3} = - \frac{x + 8}{2}

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

3 y^{3} = 3 - \frac{x + 8}{2}

Calculate

y = 3 - \frac{x + 8}{2}

Simplify the root

More Steps

Evaluate

3 - \frac{x + 8}{2}

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

\frac{3 - x - 8}{3 2}

Simplify the radical expression

\frac{- 3 x + 8}{3 2}

Simplify the radical expression

- \frac{3 x + 8}{3 2}

Multiply by the Conjugate

- \frac{3 x + 8 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Calculate

- \frac{3 x + 8 \times 3 2 ^{2}}{2}

Calculate

More Steps

Evaluate

3 x + 8 \times 3 2^{2}

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

3 (x + 8) \times 2^{2}

Calculate the product

3 4 x + 32

- \frac{3 4 x + 32}{2}

y = - \frac{3 4 x + 32}{2}

Solution

f^{- 1} (x) = - \frac{3 4 x + 32}{2}

Show Solution

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

Evaluate

y = - 2 x^{3} - 8

To test if the graph of y = - 2 x^{3} - 8 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 2 (- x)^{3} - 8

Simplify

More Steps

Evaluate

- 2 (- x)^{3} - 8

Multiply the terms

More Steps

Evaluate

- 2 (- x)^{3}

Rewrite the expression

- 2 (- x^{3})

Multiply the numbers

2 x^{3}

2 x^{3} - 8

- y = 2 x^{3} - 8

Change the signs both sides

y = - 2 x^{3} + 8

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

x = - \frac{3 4 y + 32}{2}

Evaluate

y = - 2 x^{3} - 8

Swap the sides of the equation

- 2 x^{3} - 8 = y

Move the constant to the right-hand side and change its sign

- 2 x^{3} = y + 8

Change the signs on both sides of the equation

2 x^{3} = - y - 8

Divide both sides

\frac{2 x ^{3}}{2} = \frac{- y - 8}{2}

Divide the numbers

x^{3} = \frac{- y - 8}{2}

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

x^{3} = - \frac{y + 8}{2}

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

3 x^{3} = 3 - \frac{y + 8}{2}

Calculate

x = 3 - \frac{y + 8}{2}

Solution

More Steps

Evaluate

3 - \frac{y + 8}{2}

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

\frac{3 - y - 8}{3 2}

Simplify the radical expression

\frac{- 3 y + 8}{3 2}

Simplify the radical expression

- \frac{3 y + 8}{3 2}

Multiply by the Conjugate

- \frac{3 y + 8 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Calculate

- \frac{3 y + 8 \times 3 2 ^{2}}{2}

Calculate

More Steps

Evaluate

3 y + 8 \times 3 2^{2}

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

3 (y + 8) \times 2^{2}

Calculate the product

3 4 y + 32

- \frac{3 4 y + 32}{2}

x = - \frac{3 4 y + 32}{2}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph