Solve y=-4x^212x-15

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 36 x + 540}{12}

Evaluate

y = - 4 x^{2} \times 12 x - 15

Simplify

More Steps

Evaluate

- 4 x^{2} \times 12 x - 15

Multiply

More Steps

Evaluate

- 4 x^{2} \times 12 x

Multiply the terms

- 48 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 48 x^{2 + 1}

Add the numbers

- 48 x^{3}

- 48 x^{3} - 15

y = - 48 x^{3} - 15

Interchange x and y

x = - 48 y^{3} - 15

Swap the sides of the equation

- 48 y^{3} - 15 = x

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

- 48 y^{3} = x + 15

Change the signs on both sides of the equation

48 y^{3} = - x - 15

Divide both sides

\frac{48 y ^{3}}{48} = \frac{- x - 15}{48}

Divide the numbers

y^{3} = \frac{- x - 15}{48}

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

y^{3} = - \frac{x + 15}{48}

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

3 y^{3} = 3 - \frac{x + 15}{48}

Calculate

y = 3 - \frac{x + 15}{48}

Simplify the root

More Steps

Evaluate

3 - \frac{x + 15}{48}

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

\frac{3 - x - 15}{3 48}

Simplify the radical expression

\frac{- 3 x + 15}{3 48}

Simplify the radical expression

More Steps

Evaluate

348

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 6

Write the number in exponential form with the base of 2

3 2^{3} \times 6

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

3 2^{3} \times 36

Reduce the index of the radical and exponent with 3

236

- \frac{3 x + 15}{2 3 6}

Multiply by the Conjugate

- \frac{3 x + 15 \times 3 6 ^{2}}{2 3 6 \times 3 6 ^{2}}

Calculate

- \frac{3 x + 15 \times 3 6 ^{2}}{2 \times 6}

Calculate

More Steps

Evaluate

3 x + 15 \times 3 6^{2}

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

3 (x + 15) \times 6^{2}

Calculate the product

3 36 x + 540

- \frac{3 36 x + 540}{2 \times 6}

Calculate

- \frac{3 36 x + 540}{12}

y = - \frac{3 36 x + 540}{12}

Solution

f^{- 1} (x) = - \frac{3 36 x + 540}{12}

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 = - 4 x^{2} 12 x - 15

Simplify the expression

y = - 48 x^{3} - 15

To test if the graph of y = - 48 x^{3} - 15 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 48 (- x)^{3} - 15

Simplify

More Steps

Evaluate

- 48 (- x)^{3} - 15

Multiply the terms

More Steps

Evaluate

- 48 (- x)^{3}

Rewrite the expression

- 48 (- x^{3})

Multiply the numbers

48 x^{3}

48 x^{3} - 15

- y = 48 x^{3} - 15

Change the signs both sides

y = - 48 x^{3} + 15

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = - \frac{3 36 y + 540}{12}

Evaluate

y = - 4 x^{2} \times 12 x - 15

Simplify

More Steps

Evaluate

- 4 x^{2} \times 12 x - 15

Multiply

More Steps

Evaluate

- 4 x^{2} \times 12 x

Multiply the terms

- 48 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 48 x^{2 + 1}

Add the numbers

- 48 x^{3}

- 48 x^{3} - 15

y = - 48 x^{3} - 15

Swap the sides of the equation

- 48 x^{3} - 15 = y

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

- 48 x^{3} = y + 15

Change the signs on both sides of the equation

48 x^{3} = - y - 15

Divide both sides

\frac{48 x ^{3}}{48} = \frac{- y - 15}{48}

Divide the numbers

x^{3} = \frac{- y - 15}{48}

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

x^{3} = - \frac{y + 15}{48}

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

3 x^{3} = 3 - \frac{y + 15}{48}

Calculate

x = 3 - \frac{y + 15}{48}

Solution

More Steps

Evaluate

3 - \frac{y + 15}{48}

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

\frac{3 - y - 15}{3 48}

Simplify the radical expression

\frac{- 3 y + 15}{3 48}

Simplify the radical expression

More Steps

Evaluate

348

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 6

Write the number in exponential form with the base of 2

3 2^{3} \times 6

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

3 2^{3} \times 36

Reduce the index of the radical and exponent with 3

236

- \frac{3 y + 15}{2 3 6}

Multiply by the Conjugate

- \frac{3 y + 15 \times 3 6 ^{2}}{2 3 6 \times 3 6 ^{2}}

Calculate

- \frac{3 y + 15 \times 3 6 ^{2}}{2 \times 6}

Calculate

More Steps

Evaluate

3 y + 15 \times 3 6^{2}

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

3 (y + 15) \times 6^{2}

Calculate the product

3 36 y + 540

- \frac{3 36 y + 540}{2 \times 6}

Calculate

- \frac{3 36 y + 540}{12}

x = - \frac{3 36 y + 540}{12}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph