Solve y=-5x^230x-43

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 180 x + 7740}{30}

Evaluate

y = - 5 x^{2} \times 30 x - 43

Simplify

More Steps

Evaluate

- 5 x^{2} \times 30 x - 43

Multiply

More Steps

Evaluate

- 5 x^{2} \times 30 x

Multiply the terms

- 150 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 150 x^{2 + 1}

Add the numbers

- 150 x^{3}

- 150 x^{3} - 43

y = - 150 x^{3} - 43

Interchange x and y

x = - 150 y^{3} - 43

Swap the sides of the equation

- 150 y^{3} - 43 = x

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

- 150 y^{3} = x + 43

Change the signs on both sides of the equation

150 y^{3} = - x - 43

Divide both sides

\frac{150 y ^{3}}{150} = \frac{- x - 43}{150}

Divide the numbers

y^{3} = \frac{- x - 43}{150}

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

y^{3} = - \frac{x + 43}{150}

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

3 y^{3} = 3 - \frac{x + 43}{150}

Calculate

y = 3 - \frac{x + 43}{150}

Simplify the root

More Steps

Evaluate

3 - \frac{x + 43}{150}

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

\frac{3 - x - 43}{3 150}

Simplify the radical expression

\frac{- 3 x + 43}{3 150}

Simplify the radical expression

- \frac{3 x + 43}{3 150}

Multiply by the Conjugate

- \frac{3 x + 43 \times 3 15 0 ^{2}}{3 150 \times 3 15 0 ^{2}}

Calculate

- \frac{3 x + 43 \times 3 15 0 ^{2}}{150}

Calculate

More Steps

Evaluate

3 x + 43 \times 3 15 0^{2}

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

3 (x + 43) \times 15 0^{2}

Calculate the product

3 22500 x + 967500

Factor the expression

3 22500 (x + 43)

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

322500 \times 3 x + 43

Evaluate the root

53180 \times 3 x + 43

Calculate the product

5 3 180 x + 7740

- \frac{5 3 180 x + 7740}{150}

Cancel out the common factor 5

- \frac{3 180 x + 7740}{30}

y = - \frac{3 180 x + 7740}{30}

Solution

f^{- 1} (x) = - \frac{3 180 x + 7740}{30}

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} 30 x - 43

Simplify the expression

y = - 150 x^{3} - 43

To test if the graph of y = - 150 x^{3} - 43 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = - 150 (- x)^{3} - 43

Simplify

More Steps

Evaluate

- 150 (- x)^{3} - 43

Multiply the terms

More Steps

Evaluate

- 150 (- x)^{3}

Rewrite the expression

- 150 (- x^{3})

Multiply the numbers

150 x^{3}

150 x^{3} - 43

- y = 150 x^{3} - 43

Change the signs both sides

y = - 150 x^{3} + 43

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = - \frac{3 180 y + 7740}{30}

Evaluate

y = - 5 x^{2} \times 30 x - 43

Simplify

More Steps

Evaluate

- 5 x^{2} \times 30 x - 43

Multiply

More Steps

Evaluate

- 5 x^{2} \times 30 x

Multiply the terms

- 150 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 150 x^{2 + 1}

Add the numbers

- 150 x^{3}

- 150 x^{3} - 43

y = - 150 x^{3} - 43

Swap the sides of the equation

- 150 x^{3} - 43 = y

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

- 150 x^{3} = y + 43

Change the signs on both sides of the equation

150 x^{3} = - y - 43

Divide both sides

\frac{150 x ^{3}}{150} = \frac{- y - 43}{150}

Divide the numbers

x^{3} = \frac{- y - 43}{150}

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

x^{3} = - \frac{y + 43}{150}

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

3 x^{3} = 3 - \frac{y + 43}{150}

Calculate

x = 3 - \frac{y + 43}{150}

Solution

More Steps

Evaluate

3 - \frac{y + 43}{150}

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

\frac{3 - y - 43}{3 150}

Simplify the radical expression

\frac{- 3 y + 43}{3 150}

Simplify the radical expression

- \frac{3 y + 43}{3 150}

Multiply by the Conjugate

- \frac{3 y + 43 \times 3 15 0 ^{2}}{3 150 \times 3 15 0 ^{2}}

Calculate

- \frac{3 y + 43 \times 3 15 0 ^{2}}{150}

Calculate

More Steps

Evaluate

3 y + 43 \times 3 15 0^{2}

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

3 (y + 43) \times 15 0^{2}

Calculate the product

3 22500 y + 967500

Factor the expression

3 22500 (y + 43)

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

322500 \times 3 y + 43

Evaluate the root

53180 \times 3 y + 43

Calculate the product

5 3 180 y + 7740

- \frac{5 3 180 y + 7740}{150}

Cancel out the common factor 5

- \frac{3 180 y + 7740}{30}

x = - \frac{3 180 y + 7740}{30}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph