Solve y=-x^24x-3 - ScanMath

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 2 x + 6}{2}

Evaluate

y = - x^{2} \times 4 x - 3

Simplify

More Steps

Evaluate

- x^{2} \times 4 x - 3

Multiply

More Steps

Evaluate

- x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 4

Add the numbers

- x^{3} \times 4

Use the commutative property to reorder the terms

- 4 x^{3}

- 4 x^{3} - 3

y = - 4 x^{3} - 3

Interchange x and y

x = - 4 y^{3} - 3

Swap the sides of the equation

- 4 y^{3} - 3 = x

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

- 4 y^{3} = x + 3

Change the signs on both sides of the equation

4 y^{3} = - x - 3

Divide both sides

\frac{4 y ^{3}}{4} = \frac{- x - 3}{4}

Divide the numbers

y^{3} = \frac{- x - 3}{4}

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

y^{3} = - \frac{x + 3}{4}

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

3 y^{3} = 3 - \frac{x + 3}{4}

Calculate

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

Simplify the root

More Steps

Evaluate

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

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

\frac{3 - x - 3}{3 4}

Simplify the radical expression

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

Simplify the radical expression

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

Multiply by the Conjugate

- \frac{3 x + 3 \times 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Calculate

- \frac{3 x + 3 \times 3 4 ^{2}}{2 ^{2}}

Calculate

More Steps

Evaluate

3 x + 3 \times 3 4^{2}

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

3 (x + 3) \times 4^{2}

Calculate the product

3 16 x + 48

Factor the expression

3 16 (x + 3)

The root of a product is equal to the product of the roots of each factor

316 \times 3 x + 3

Evaluate the root

232 \times 3 x + 3

Calculate the product

2 3 2 x + 6

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

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

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

y = - \frac{3 2 x + 6}{2}

Solution

f^{- 1} (x) = - \frac{3 2 x + 6}{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 = - x^{2} 4 x - 3

Simplify the expression

y = - 4 x^{3} - 3

To test if the graph of y = - 4 x^{3} - 3 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 4 (- x)^{3} - 3

Simplify

More Steps

Evaluate

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

Multiply the terms

More Steps

Evaluate

- 4 (- x)^{3}

Rewrite the expression

- 4 (- x^{3})

Multiply the numbers

4 x^{3}

4 x^{3} - 3

- y = 4 x^{3} - 3

Change the signs both sides

y = - 4 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 2 y + 6}{2}

Evaluate

y = - x^{2} \times 4 x - 3

Simplify

More Steps

Evaluate

- x^{2} \times 4 x - 3

Multiply

More Steps

Evaluate

- x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 4

Add the numbers

- x^{3} \times 4

Use the commutative property to reorder the terms

- 4 x^{3}

- 4 x^{3} - 3

y = - 4 x^{3} - 3

Swap the sides of the equation

- 4 x^{3} - 3 = y

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

- 4 x^{3} = y + 3

Change the signs on both sides of the equation

4 x^{3} = - y - 3

Divide both sides

\frac{4 x ^{3}}{4} = \frac{- y - 3}{4}

Divide the numbers

x^{3} = \frac{- y - 3}{4}

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

x^{3} = - \frac{y + 3}{4}

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

3 x^{3} = 3 - \frac{y + 3}{4}

Calculate

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

Solution

More Steps

Evaluate

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

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

\frac{3 - y - 3}{3 4}

Simplify the radical expression

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

Simplify the radical expression

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

Multiply by the Conjugate

- \frac{3 y + 3 \times 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Calculate

- \frac{3 y + 3 \times 3 4 ^{2}}{2 ^{2}}

Calculate

More Steps

Evaluate

3 y + 3 \times 3 4^{2}

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

3 (y + 3) \times 4^{2}

Calculate the product

3 16 y + 48

Factor the expression

3 16 (y + 3)

The root of a product is equal to the product of the roots of each factor

316 \times 3 y + 3

Evaluate the root

232 \times 3 y + 3

Calculate the product

2 3 2 y + 6

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

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

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

x = - \frac{3 2 y + 6}{2}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph