Solve y=-5x^210x-14

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 20 x + 280}{10}

Evaluate

y = - 5 x^{2} \times 10 x - 14

Simplify

More Steps

Evaluate

- 5 x^{2} \times 10 x - 14

Multiply

More Steps

Evaluate

- 5 x^{2} \times 10 x

Multiply the terms

- 50 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 50 x^{2 + 1}

Add the numbers

- 50 x^{3}

- 50 x^{3} - 14

y = - 50 x^{3} - 14

Interchange x and y

x = - 50 y^{3} - 14

Swap the sides of the equation

- 50 y^{3} - 14 = x

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

- 50 y^{3} = x + 14

Change the signs on both sides of the equation

50 y^{3} = - x - 14

Divide both sides

\frac{50 y ^{3}}{50} = \frac{- x - 14}{50}

Divide the numbers

y^{3} = \frac{- x - 14}{50}

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

y^{3} = - \frac{x + 14}{50}

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

3 y^{3} = 3 - \frac{x + 14}{50}

Calculate

y = 3 - \frac{x + 14}{50}

Simplify the root

More Steps

Evaluate

3 - \frac{x + 14}{50}

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

\frac{3 - x - 14}{3 50}

Simplify the radical expression

\frac{- 3 x + 14}{3 50}

Simplify the radical expression

- \frac{3 x + 14}{3 50}

Multiply by the Conjugate

- \frac{3 x + 14 \times 3 5 0 ^{2}}{3 50 \times 3 5 0 ^{2}}

Calculate

- \frac{3 x + 14 \times 3 5 0 ^{2}}{50}

Calculate

More Steps

Evaluate

3 x + 14 \times 3 5 0^{2}

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

3 (x + 14) \times 5 0^{2}

Calculate the product

3 2500 x + 35000

Factor the expression

3 2500 (x + 14)

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

32500 \times 3 x + 14

Evaluate the root

5320 \times 3 x + 14

Calculate the product

5 3 20 x + 280

- \frac{5 3 20 x + 280}{50}

Cancel out the common factor 5

- \frac{3 20 x + 280}{10}

y = - \frac{3 20 x + 280}{10}

Solution

f^{- 1} (x) = - \frac{3 20 x + 280}{10}

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 = - 5 x^{2} 10 x - 14

Simplify the expression

y = - 50 x^{3} - 14

To test if the graph of y = - 50 x^{3} - 14 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 50 (- x)^{3} - 14

Simplify

More Steps

Evaluate

- 50 (- x)^{3} - 14

Multiply the terms

More Steps

Evaluate

- 50 (- x)^{3}

Rewrite the expression

- 50 (- x^{3})

Multiply the numbers

50 x^{3}

50 x^{3} - 14

- y = 50 x^{3} - 14

Change the signs both sides

y = - 50 x^{3} + 14

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = - \frac{3 20 y + 280}{10}

Evaluate

y = - 5 x^{2} \times 10 x - 14

Simplify

More Steps

Evaluate

- 5 x^{2} \times 10 x - 14

Multiply

More Steps

Evaluate

- 5 x^{2} \times 10 x

Multiply the terms

- 50 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 50 x^{2 + 1}

Add the numbers

- 50 x^{3}

- 50 x^{3} - 14

y = - 50 x^{3} - 14

Swap the sides of the equation

- 50 x^{3} - 14 = y

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

- 50 x^{3} = y + 14

Change the signs on both sides of the equation

50 x^{3} = - y - 14

Divide both sides

\frac{50 x ^{3}}{50} = \frac{- y - 14}{50}

Divide the numbers

x^{3} = \frac{- y - 14}{50}

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

x^{3} = - \frac{y + 14}{50}

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

3 x^{3} = 3 - \frac{y + 14}{50}

Calculate

x = 3 - \frac{y + 14}{50}

Solution

More Steps

Evaluate

3 - \frac{y + 14}{50}

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

\frac{3 - y - 14}{3 50}

Simplify the radical expression

\frac{- 3 y + 14}{3 50}

Simplify the radical expression

- \frac{3 y + 14}{3 50}

Multiply by the Conjugate

- \frac{3 y + 14 \times 3 5 0 ^{2}}{3 50 \times 3 5 0 ^{2}}

Calculate

- \frac{3 y + 14 \times 3 5 0 ^{2}}{50}

Calculate

More Steps

Evaluate

3 y + 14 \times 3 5 0^{2}

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

3 (y + 14) \times 5 0^{2}

Calculate the product

3 2500 y + 35000

Factor the expression

3 2500 (y + 14)

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

32500 \times 3 y + 14

Evaluate the root

5320 \times 3 y + 14

Calculate the product

5 3 20 y + 280

- \frac{5 3 20 y + 280}{50}

Cancel out the common factor 5

- \frac{3 20 y + 280}{10}

x = - \frac{3 20 y + 280}{10}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph