Solve y = -x^223x - 132

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 529 x + 69828}{23}

Evaluate

y = - x^{2} \times 23 x - 132

Simplify

More Steps

Evaluate

- x^{2} \times 23 x - 132

Multiply

More Steps

Evaluate

- x^{2} \times 23 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 23

Add the numbers

- x^{3} \times 23

Use the commutative property to reorder the terms

- 23 x^{3}

- 23 x^{3} - 132

y = - 23 x^{3} - 132

Interchange x and y

x = - 23 y^{3} - 132

Swap the sides of the equation

- 23 y^{3} - 132 = x

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

- 23 y^{3} = x + 132

Change the signs on both sides of the equation

23 y^{3} = - x - 132

Divide both sides

\frac{23 y ^{3}}{23} = \frac{- x - 132}{23}

Divide the numbers

y^{3} = \frac{- x - 132}{23}

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

y^{3} = - \frac{x + 132}{23}

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

3 y^{3} = 3 - \frac{x + 132}{23}

Calculate

y = 3 - \frac{x + 132}{23}

Simplify the root

More Steps

Evaluate

3 - \frac{x + 132}{23}

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

\frac{3 - x - 132}{3 23}

Simplify the radical expression

\frac{- 3 x + 132}{3 23}

Simplify the radical expression

- \frac{3 x + 132}{3 23}

Multiply by the Conjugate

- \frac{3 x + 132 \times 3 2 3 ^{2}}{3 23 \times 3 2 3 ^{2}}

Calculate

- \frac{3 x + 132 \times 3 2 3 ^{2}}{23}

Calculate

More Steps

Evaluate

3 x + 132 \times 3 2 3^{2}

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

3 (x + 132) \times 2 3^{2}

Calculate the product

3 529 x + 69828

- \frac{3 529 x + 69828}{23}

y = - \frac{3 529 x + 69828}{23}

Solution

f^{- 1} (x) = - \frac{3 529 x + 69828}{23}

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 = - x^{2} 23 x - 132

Simplify the expression

y = - 23 x^{3} - 132

To test if the graph of y = - 23 x^{3} - 132 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 23 (- x)^{3} - 132

Simplify

More Steps

Evaluate

- 23 (- x)^{3} - 132

Multiply the terms

More Steps

Evaluate

- 23 (- x)^{3}

Rewrite the expression

- 23 (- x^{3})

Multiply the numbers

23 x^{3}

23 x^{3} - 132

- y = 23 x^{3} - 132

Change the signs both sides

y = - 23 x^{3} + 132

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = - \frac{3 529 y + 69828}{23}

Evaluate

y = - x^{2} \times 23 x - 132

Simplify

More Steps

Evaluate

- x^{2} \times 23 x - 132

Multiply

More Steps

Evaluate

- x^{2} \times 23 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 23

Add the numbers

- x^{3} \times 23

Use the commutative property to reorder the terms

- 23 x^{3}

- 23 x^{3} - 132

y = - 23 x^{3} - 132

Swap the sides of the equation

- 23 x^{3} - 132 = y

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

- 23 x^{3} = y + 132

Change the signs on both sides of the equation

23 x^{3} = - y - 132

Divide both sides

\frac{23 x ^{3}}{23} = \frac{- y - 132}{23}

Divide the numbers

x^{3} = \frac{- y - 132}{23}

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

x^{3} = - \frac{y + 132}{23}

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

3 x^{3} = 3 - \frac{y + 132}{23}

Calculate

x = 3 - \frac{y + 132}{23}

Solution

More Steps

Evaluate

3 - \frac{y + 132}{23}

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

\frac{3 - y - 132}{3 23}

Simplify the radical expression

\frac{- 3 y + 132}{3 23}

Simplify the radical expression

- \frac{3 y + 132}{3 23}

Multiply by the Conjugate

- \frac{3 y + 132 \times 3 2 3 ^{2}}{3 23 \times 3 2 3 ^{2}}

Calculate

- \frac{3 y + 132 \times 3 2 3 ^{2}}{23}

Calculate

More Steps

Evaluate

3 y + 132 \times 3 2 3^{2}

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

3 (y + 132) \times 2 3^{2}

Calculate the product

3 529 y + 69828

- \frac{3 529 y + 69828}{23}

x = - \frac{3 529 y + 69828}{23}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph