Solve y=-42x^2 500x-80

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 441 x + 35280}{210}

Evaluate

y = - 42 x^{2} \times 500 x - 80

Simplify

More Steps

Evaluate

- 42 x^{2} \times 500 x - 80

Multiply

More Steps

Evaluate

- 42 x^{2} \times 500 x

Multiply the terms

- 21000 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 21000 x^{2 + 1}

Add the numbers

- 21000 x^{3}

- 21000 x^{3} - 80

y = - 21000 x^{3} - 80

Interchange x and y

x = - 21000 y^{3} - 80

Swap the sides of the equation

- 21000 y^{3} - 80 = x

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

- 21000 y^{3} = x + 80

Change the signs on both sides of the equation

21000 y^{3} = - x - 80

Divide both sides

\frac{21000 y ^{3}}{21000} = \frac{- x - 80}{21000}

Divide the numbers

y^{3} = \frac{- x - 80}{21000}

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

y^{3} = - \frac{x + 80}{21000}

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

3 y^{3} = 3 - \frac{x + 80}{21000}

Calculate

y = 3 - \frac{x + 80}{21000}

Simplify the root

More Steps

Evaluate

3 - \frac{x + 80}{21000}

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

\frac{3 - x - 80}{3 21000}

Simplify the radical expression

\frac{- 3 x + 80}{3 21000}

Simplify the radical expression

More Steps

Evaluate

321000

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

3 1000 \times 21

Write the number in exponential form with the base of 10

3 1 0^{3} \times 21

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

3 1 0^{3} \times 321

Reduce the index of the radical and exponent with 3

10321

- \frac{3 x + 80}{10 3 21}

Multiply by the Conjugate

- \frac{3 x + 80 \times 3 2 1 ^{2}}{10 3 21 \times 3 2 1 ^{2}}

Calculate

- \frac{3 x + 80 \times 3 2 1 ^{2}}{10 \times 21}

Calculate

More Steps

Evaluate

3 x + 80 \times 3 2 1^{2}

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

3 (x + 80) \times 2 1^{2}

Calculate the product

3 441 x + 35280

- \frac{3 441 x + 35280}{10 \times 21}

Calculate

- \frac{3 441 x + 35280}{210}

y = - \frac{3 441 x + 35280}{210}

Solution

f^{- 1} (x) = - \frac{3 441 x + 35280}{210}

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 = - 42 x^{2} 500 x - 80

Simplify the expression

y = - 21000 x^{3} - 80

To test if the graph of y = - 21000 x^{3} - 80 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 21000 (- x)^{3} - 80

Simplify

More Steps

Evaluate

- 21000 (- x)^{3} - 80

Multiply the terms

More Steps

Evaluate

- 21000 (- x)^{3}

Rewrite the expression

- 21000 (- x^{3})

Multiply the numbers

21000 x^{3}

21000 x^{3} - 80

- y = 21000 x^{3} - 80

Change the signs both sides

y = - 21000 x^{3} + 80

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = - \frac{3 441 y + 35280}{210}

Evaluate

y = - 42 x^{2} \times 500 x - 80

Simplify

More Steps

Evaluate

- 42 x^{2} \times 500 x - 80

Multiply

More Steps

Evaluate

- 42 x^{2} \times 500 x

Multiply the terms

- 21000 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 21000 x^{2 + 1}

Add the numbers

- 21000 x^{3}

- 21000 x^{3} - 80

y = - 21000 x^{3} - 80

Swap the sides of the equation

- 21000 x^{3} - 80 = y

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

- 21000 x^{3} = y + 80

Change the signs on both sides of the equation

21000 x^{3} = - y - 80

Divide both sides

\frac{21000 x ^{3}}{21000} = \frac{- y - 80}{21000}

Divide the numbers

x^{3} = \frac{- y - 80}{21000}

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

x^{3} = - \frac{y + 80}{21000}

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

3 x^{3} = 3 - \frac{y + 80}{21000}

Calculate

x = 3 - \frac{y + 80}{21000}

Solution

More Steps

Evaluate

3 - \frac{y + 80}{21000}

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

\frac{3 - y - 80}{3 21000}

Simplify the radical expression

\frac{- 3 y + 80}{3 21000}

Simplify the radical expression

More Steps

Evaluate

321000

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

3 1000 \times 21

Write the number in exponential form with the base of 10

3 1 0^{3} \times 21

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

3 1 0^{3} \times 321

Reduce the index of the radical and exponent with 3

10321

- \frac{3 y + 80}{10 3 21}

Multiply by the Conjugate

- \frac{3 y + 80 \times 3 2 1 ^{2}}{10 3 21 \times 3 2 1 ^{2}}

Calculate

- \frac{3 y + 80 \times 3 2 1 ^{2}}{10 \times 21}

Calculate

More Steps

Evaluate

3 y + 80 \times 3 2 1^{2}

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

3 (y + 80) \times 2 1^{2}

Calculate the product

3 441 y + 35280

- \frac{3 441 y + 35280}{10 \times 21}

Calculate

- \frac{3 441 y + 35280}{210}

x = - \frac{3 441 y + 35280}{210}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph