Solve y=-x^213x-46

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 169 x + 7774}{13}

Evaluate

y = - x^{2} \times 13 x - 46

Simplify

More Steps

Evaluate

- x^{2} \times 13 x - 46

Multiply

More Steps

Evaluate

- x^{2} \times 13 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 13

Add the numbers

- x^{3} \times 13

Use the commutative property to reorder the terms

- 13 x^{3}

- 13 x^{3} - 46

y = - 13 x^{3} - 46

Interchange x and y

x = - 13 y^{3} - 46

Swap the sides of the equation

- 13 y^{3} - 46 = x

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

- 13 y^{3} = x + 46

Change the signs on both sides of the equation

13 y^{3} = - x - 46

Divide both sides

\frac{13 y ^{3}}{13} = \frac{- x - 46}{13}

Divide the numbers

y^{3} = \frac{- x - 46}{13}

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

y^{3} = - \frac{x + 46}{13}

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

3 y^{3} = 3 - \frac{x + 46}{13}

Calculate

y = 3 - \frac{x + 46}{13}

Simplify the root

More Steps

Evaluate

3 - \frac{x + 46}{13}

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

\frac{3 - x - 46}{3 13}

Simplify the radical expression

\frac{- 3 x + 46}{3 13}

Simplify the radical expression

- \frac{3 x + 46}{3 13}

Multiply by the Conjugate

- \frac{3 x + 46 \times 3 1 3 ^{2}}{3 13 \times 3 1 3 ^{2}}

Calculate

- \frac{3 x + 46 \times 3 1 3 ^{2}}{13}

Calculate

More Steps

Evaluate

3 x + 46 \times 3 1 3^{2}

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

3 (x + 46) \times 1 3^{2}

Calculate the product

3 169 x + 7774

- \frac{3 169 x + 7774}{13}

y = - \frac{3 169 x + 7774}{13}

Solution

f^{- 1} (x) = - \frac{3 169 x + 7774}{13}

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} 13 x - 46

Simplify the expression

y = - 13 x^{3} - 46

To test if the graph of y = - 13 x^{3} - 46 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 13 (- x)^{3} - 46

Simplify

More Steps

Evaluate

- 13 (- x)^{3} - 46

Multiply the terms

More Steps

Evaluate

- 13 (- x)^{3}

Rewrite the expression

- 13 (- x^{3})

Multiply the numbers

13 x^{3}

13 x^{3} - 46

- y = 13 x^{3} - 46

Change the signs both sides

y = - 13 x^{3} + 46

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = - \frac{3 169 y + 7774}{13}

Evaluate

y = - x^{2} \times 13 x - 46

Simplify

More Steps

Evaluate

- x^{2} \times 13 x - 46

Multiply

More Steps

Evaluate

- x^{2} \times 13 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 13

Add the numbers

- x^{3} \times 13

Use the commutative property to reorder the terms

- 13 x^{3}

- 13 x^{3} - 46

y = - 13 x^{3} - 46

Swap the sides of the equation

- 13 x^{3} - 46 = y

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

- 13 x^{3} = y + 46

Change the signs on both sides of the equation

13 x^{3} = - y - 46

Divide both sides

\frac{13 x ^{3}}{13} = \frac{- y - 46}{13}

Divide the numbers

x^{3} = \frac{- y - 46}{13}

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

x^{3} = - \frac{y + 46}{13}

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

3 x^{3} = 3 - \frac{y + 46}{13}

Calculate

x = 3 - \frac{y + 46}{13}

Solution

More Steps

Evaluate

3 - \frac{y + 46}{13}

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

\frac{3 - y - 46}{3 13}

Simplify the radical expression

\frac{- 3 y + 46}{3 13}

Simplify the radical expression

- \frac{3 y + 46}{3 13}

Multiply by the Conjugate

- \frac{3 y + 46 \times 3 1 3 ^{2}}{3 13 \times 3 1 3 ^{2}}

Calculate

- \frac{3 y + 46 \times 3 1 3 ^{2}}{13}

Calculate

More Steps

Evaluate

3 y + 46 \times 3 1 3^{2}

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

3 (y + 46) \times 1 3^{2}

Calculate the product

3 169 y + 7774

- \frac{3 169 y + 7774}{13}

x = - \frac{3 169 y + 7774}{13}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph