Solve y= 5-5x x^2

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = \frac{3 - 25 x + 125}{5}

Evaluate

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

Simplify

More Steps

Evaluate

5 - 5 x \times x^{2}

Multiply

More Steps

Evaluate

5 x \times x^{2}

Multiply the terms with the same base by adding their exponents

5 x^{1 + 2}

Add the numbers

5 x^{3}

5 - 5 x^{3}

y = 5 - 5 x^{3}

Interchange x and y

x = 5 - 5 y^{3}

Swap the sides of the equation

5 - 5 y^{3} = x

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

- 5 y^{3} = x - 5

Change the signs on both sides of the equation

5 y^{3} = - x + 5

Divide both sides

\frac{5 y ^{3}}{5} = \frac{- x + 5}{5}

Divide the numbers

y^{3} = \frac{- x + 5}{5}

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

3 y^{3} = 3 \frac{- x + 5}{5}

Calculate

y = 3 \frac{- x + 5}{5}

Simplify the root

More Steps

Evaluate

3 \frac{- x + 5}{5}

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

\frac{3 - x + 5}{3 5}

Multiply by the Conjugate

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

Calculate

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

Calculate

More Steps

Evaluate

3 - x + 5 \times 3 5^{2}

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

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

Calculate the product

3 - 25 x + 125

\frac{3 - 25 x + 125}{5}

y = \frac{3 - 25 x + 125}{5}

Solution

f^{- 1} (x) = \frac{3 - 25 x + 125}{5}

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 - 5 x x^{2}

Simplify the expression

y = 5 - 5 x^{3}

To test if the graph of y = 5 - 5 x^{3} is symmetry with respect to the origin,substitute -x for x and -y for y

- y = 5 - 5 (- x)^{3}

Simplify

More Steps

Evaluate

5 - 5 (- x)^{3}

Multiply the terms

More Steps

Evaluate

5 (- x)^{3}

Rewrite the expression

5 (- x^{3})

Multiply the numbers

- 5 x^{3}

5 - (- 5 x^{3})

Rewrite the expression

5 + 5 x^{3}

- y = 5 + 5 x^{3}

Change the signs both sides

y = - 5 - 5 x^{3}

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{3 - 25 y + 125}{5}

Evaluate

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

Simplify

More Steps

Evaluate

5 - 5 x \times x^{2}

Multiply

More Steps

Evaluate

5 x \times x^{2}

Multiply the terms with the same base by adding their exponents

5 x^{1 + 2}

Add the numbers

5 x^{3}

5 - 5 x^{3}

y = 5 - 5 x^{3}

Swap the sides of the equation

5 - 5 x^{3} = y

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

- 5 x^{3} = y - 5

Change the signs on both sides of the equation

5 x^{3} = - y + 5

Divide both sides

\frac{5 x ^{3}}{5} = \frac{- y + 5}{5}

Divide the numbers

x^{3} = \frac{- y + 5}{5}

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

3 x^{3} = 3 \frac{- y + 5}{5}

Calculate

x = 3 \frac{- y + 5}{5}

Solution

More Steps

Evaluate

3 \frac{- y + 5}{5}

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

\frac{3 - y + 5}{3 5}

Multiply by the Conjugate

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

Calculate

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

Calculate

More Steps

Evaluate

3 - y + 5 \times 3 5^{2}

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

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

Calculate the product

3 - 25 y + 125

\frac{3 - 25 y + 125}{5}

x = \frac{3 - 25 y + 125}{5}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph