Solve y = -x^211x - 30

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 121 x + 3630}{11}

Evaluate

y = - x^{2} \times 11 x - 30

Simplify

More Steps

Evaluate

- x^{2} \times 11 x - 30

Multiply

More Steps

Evaluate

- x^{2} \times 11 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 11

Add the numbers

- x^{3} \times 11

Use the commutative property to reorder the terms

- 11 x^{3}

- 11 x^{3} - 30

y = - 11 x^{3} - 30

Interchange x and y

x = - 11 y^{3} - 30

Swap the sides of the equation

- 11 y^{3} - 30 = x

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

- 11 y^{3} = x + 30

Change the signs on both sides of the equation

11 y^{3} = - x - 30

Divide both sides

\frac{11 y ^{3}}{11} = \frac{- x - 30}{11}

Divide the numbers

y^{3} = \frac{- x - 30}{11}

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

y^{3} = - \frac{x + 30}{11}

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

3 y^{3} = 3 - \frac{x + 30}{11}

Calculate

y = 3 - \frac{x + 30}{11}

Simplify the root

More Steps

Evaluate

3 - \frac{x + 30}{11}

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

\frac{3 - x - 30}{3 11}

Simplify the radical expression

\frac{- 3 x + 30}{3 11}

Simplify the radical expression

- \frac{3 x + 30}{3 11}

Multiply by the Conjugate

- \frac{3 x + 30 \times 3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Calculate

- \frac{3 x + 30 \times 3 1 1 ^{2}}{11}

Calculate

More Steps

Evaluate

3 x + 30 \times 3 1 1^{2}

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

3 (x + 30) \times 1 1^{2}

Calculate the product

3 121 x + 3630

- \frac{3 121 x + 3630}{11}

y = - \frac{3 121 x + 3630}{11}

Solution

f^{- 1} (x) = - \frac{3 121 x + 3630}{11}

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} 11 x - 30

Simplify the expression

y = - 11 x^{3} - 30

To test if the graph of y = - 11 x^{3} - 30 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 11 (- x)^{3} - 30

Simplify

More Steps

Evaluate

- 11 (- x)^{3} - 30

Multiply the terms

More Steps

Evaluate

- 11 (- x)^{3}

Rewrite the expression

- 11 (- x^{3})

Multiply the numbers

11 x^{3}

11 x^{3} - 30

- y = 11 x^{3} - 30

Change the signs both sides

y = - 11 x^{3} + 30

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = - \frac{3 121 y + 3630}{11}

Evaluate

y = - x^{2} \times 11 x - 30

Simplify

More Steps

Evaluate

- x^{2} \times 11 x - 30

Multiply

More Steps

Evaluate

- x^{2} \times 11 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 11

Add the numbers

- x^{3} \times 11

Use the commutative property to reorder the terms

- 11 x^{3}

- 11 x^{3} - 30

y = - 11 x^{3} - 30

Swap the sides of the equation

- 11 x^{3} - 30 = y

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

- 11 x^{3} = y + 30

Change the signs on both sides of the equation

11 x^{3} = - y - 30

Divide both sides

\frac{11 x ^{3}}{11} = \frac{- y - 30}{11}

Divide the numbers

x^{3} = \frac{- y - 30}{11}

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

x^{3} = - \frac{y + 30}{11}

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

3 x^{3} = 3 - \frac{y + 30}{11}

Calculate

x = 3 - \frac{y + 30}{11}

Solution

More Steps

Evaluate

3 - \frac{y + 30}{11}

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

\frac{3 - y - 30}{3 11}

Simplify the radical expression

\frac{- 3 y + 30}{3 11}

Simplify the radical expression

- \frac{3 y + 30}{3 11}

Multiply by the Conjugate

- \frac{3 y + 30 \times 3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Calculate

- \frac{3 y + 30 \times 3 1 1 ^{2}}{11}

Calculate

More Steps

Evaluate

3 y + 30 \times 3 1 1^{2}

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

3 (y + 30) \times 1 1^{2}

Calculate the product

3 121 y + 3630

- \frac{3 121 y + 3630}{11}

x = - \frac{3 121 y + 3630}{11}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph