Solve y=-x^2 6x-3

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 36 x + 108}{6}

Evaluate

y = - x^{2} \times 6 x - 3

Simplify

More Steps

Evaluate

- x^{2} \times 6 x - 3

Multiply

More Steps

Evaluate

- x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 6

Add the numbers

- x^{3} \times 6

Use the commutative property to reorder the terms

- 6 x^{3}

- 6 x^{3} - 3

y = - 6 x^{3} - 3

Interchange x and y

x = - 6 y^{3} - 3

Swap the sides of the equation

- 6 y^{3} - 3 = x

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

- 6 y^{3} = x + 3

Change the signs on both sides of the equation

6 y^{3} = - x - 3

Divide both sides

\frac{6 y ^{3}}{6} = \frac{- x - 3}{6}

Divide the numbers

y^{3} = \frac{- x - 3}{6}

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

y^{3} = - \frac{x + 3}{6}

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

3 y^{3} = 3 - \frac{x + 3}{6}

Calculate

y = 3 - \frac{x + 3}{6}

Simplify the root

More Steps

Evaluate

3 - \frac{x + 3}{6}

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

\frac{3 - x - 3}{3 6}

Simplify the radical expression

\frac{- 3 x + 3}{3 6}

Simplify the radical expression

- \frac{3 x + 3}{3 6}

Multiply by the Conjugate

- \frac{3 x + 3 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Calculate

- \frac{3 x + 3 \times 3 6 ^{2}}{6}

Calculate

More Steps

Evaluate

3 x + 3 \times 3 6^{2}

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

3 (x + 3) \times 6^{2}

Calculate the product

3 36 x + 108

- \frac{3 36 x + 108}{6}

y = - \frac{3 36 x + 108}{6}

Solution

f^{- 1} (x) = - \frac{3 36 x + 108}{6}

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} 6 x - 3

Simplify the expression

y = - 6 x^{3} - 3

To test if the graph of y = - 6 x^{3} - 3 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 6 (- x)^{3} - 3

Simplify

More Steps

Evaluate

- 6 (- x)^{3} - 3

Multiply the terms

More Steps

Evaluate

- 6 (- x)^{3}

Rewrite the expression

- 6 (- x^{3})

Multiply the numbers

6 x^{3}

6 x^{3} - 3

- y = 6 x^{3} - 3

Change the signs both sides

y = - 6 x^{3} + 3

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = - \frac{3 36 y + 108}{6}

Evaluate

y = - x^{2} \times 6 x - 3

Simplify

More Steps

Evaluate

- x^{2} \times 6 x - 3

Multiply

More Steps

Evaluate

- x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 6

Add the numbers

- x^{3} \times 6

Use the commutative property to reorder the terms

- 6 x^{3}

- 6 x^{3} - 3

y = - 6 x^{3} - 3

Swap the sides of the equation

- 6 x^{3} - 3 = y

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

- 6 x^{3} = y + 3

Change the signs on both sides of the equation

6 x^{3} = - y - 3

Divide both sides

\frac{6 x ^{3}}{6} = \frac{- y - 3}{6}

Divide the numbers

x^{3} = \frac{- y - 3}{6}

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

x^{3} = - \frac{y + 3}{6}

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

3 x^{3} = 3 - \frac{y + 3}{6}

Calculate

x = 3 - \frac{y + 3}{6}

Solution

More Steps

Evaluate

3 - \frac{y + 3}{6}

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

\frac{3 - y - 3}{3 6}

Simplify the radical expression

\frac{- 3 y + 3}{3 6}

Simplify the radical expression

- \frac{3 y + 3}{3 6}

Multiply by the Conjugate

- \frac{3 y + 3 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Calculate

- \frac{3 y + 3 \times 3 6 ^{2}}{6}

Calculate

More Steps

Evaluate

3 y + 3 \times 3 6^{2}

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

3 (y + 3) \times 6^{2}

Calculate the product

3 36 y + 108

- \frac{3 36 y + 108}{6}

x = - \frac{3 36 y + 108}{6}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph