Solve y= - 5x^220x-23

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = - \frac{3 10 x + 230}{10}

Evaluate

y = - 5 x^{2} \times 20 x - 23

Simplify

More Steps

y = - 100 x^{3} - 23

Interchange x and y

x = - 100 y^{3} - 23

Swap the sides of the equation

- 100 y^{3} - 23 = x

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

- 100 y^{3} = x + 23

Change the signs on both sides of the equation

100 y^{3} = - x - 23

Divide both sides

\frac{100 y ^{3}}{100} = \frac{- x - 23}{100}

Divide the numbers

y^{3} = \frac{- x - 23}{100}

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

y^{3} = - \frac{x + 23}{100}

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

3 y^{3} = 3 - \frac{x + 23}{100}

Calculate

y = 3 - \frac{x + 23}{100}

Simplify the root

More Steps

y = - 1 0^{- 1} 3 10 x + 230

Rewrite the expression

More Steps

y = - \frac{3 10 x + 230}{10}

Solution

f^{- 1} (x) = - \frac{3 10 x + 230}{10}

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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

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Solve for x

Solve for y

x = - \frac{3 10 y + 230}{10}

Evaluate

y = - 5 x^{2} \times 20 x - 23

Simplify

More Steps

y = - 100 x^{3} - 23

Swap the sides of the equation

- 100 x^{3} - 23 = y

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

- 100 x^{3} = y + 23

Change the signs on both sides of the equation

100 x^{3} = - y - 23

Divide both sides

\frac{100 x ^{3}}{100} = \frac{- y - 23}{100}

Divide the numbers

x^{3} = \frac{- y - 23}{100}

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

x^{3} = - \frac{y + 23}{100}

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

3 x^{3} = 3 - \frac{y + 23}{100}

Calculate

x = 3 - \frac{y + 23}{100}

Simplify the root

More Steps

x = - 1 0^{- 1} 3 10 y + 230

Solution

More Steps

x = - \frac{3 10 y + 230}{10}

Show Solution