Solve y=x^33x^2-4

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = \frac{5 81 x + 324}{3}

Evaluate

y = x^{3} \times 3 x^{2} - 4

Simplify

More Steps

Evaluate

x^{3} \times 3 x^{2} - 4

Multiply

More Steps

Evaluate

x^{3} \times 3 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 3

Add the numbers

x^{5} \times 3

Use the commutative property to reorder the terms

3 x^{5}

3 x^{5} - 4

y = 3 x^{5} - 4

Interchange x and y

x = 3 y^{5} - 4

Swap the sides of the equation

3 y^{5} - 4 = x

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

3 y^{5} = x + 4

Divide both sides

\frac{3 y ^{5}}{3} = \frac{x + 4}{3}

Divide the numbers

y^{5} = \frac{x + 4}{3}

Take the 5 -th root on both sides of the equation

5 y^{5} = 5 \frac{x + 4}{3}

Calculate

y = 5 \frac{x + 4}{3}

Simplify the root

More Steps

Evaluate

5 \frac{x + 4}{3}

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

\frac{5 x + 4}{5 3}

Multiply by the Conjugate

\frac{5 x + 4 \times 5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Calculate

\frac{5 x + 4 \times 5 3 ^{4}}{3}

Calculate

More Steps

Evaluate

5 x + 4 \times 5 3^{4}

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

5 (x + 4) \times 3^{4}

Calculate the product

5 81 x + 324

\frac{5 81 x + 324}{3}

y = \frac{5 81 x + 324}{3}

Solution

f^{- 1} (x) = \frac{5 81 x + 324}{3}

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 = x^{3} 3 x^{2} - 4

Simplify the expression

y = 3 x^{5} - 4

To test if the graph of y = 3 x^{5} - 4 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = 3 (- x)^{5} - 4

Simplify

More Steps

Evaluate

3 (- x)^{5} - 4

Multiply the terms

More Steps

Evaluate

3 (- x)^{5}

Rewrite the expression

3 (- x^{5})

Multiply the numbers

- 3 x^{5}

- 3 x^{5} - 4

- y = - 3 x^{5} - 4

Change the signs both sides

y = 3 x^{5} + 4

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{5 81 y + 324}{3}

Evaluate

y = x^{3} \times 3 x^{2} - 4

Simplify

More Steps

Evaluate

x^{3} \times 3 x^{2} - 4

Multiply

More Steps

Evaluate

x^{3} \times 3 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 3

Add the numbers

x^{5} \times 3

Use the commutative property to reorder the terms

3 x^{5}

3 x^{5} - 4

y = 3 x^{5} - 4

Swap the sides of the equation

3 x^{5} - 4 = y

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

3 x^{5} = y + 4

Divide both sides

\frac{3 x ^{5}}{3} = \frac{y + 4}{3}

Divide the numbers

x^{5} = \frac{y + 4}{3}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{y + 4}{3}

Calculate

x = 5 \frac{y + 4}{3}

Solution

More Steps

Evaluate

5 \frac{y + 4}{3}

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

\frac{5 y + 4}{5 3}

Multiply by the Conjugate

\frac{5 y + 4 \times 5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Calculate

\frac{5 y + 4 \times 5 3 ^{4}}{3}

Calculate

More Steps

Evaluate

5 y + 4 \times 5 3^{4}

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

5 (y + 4) \times 3^{4}

Calculate the product

5 81 y + 324

\frac{5 81 y + 324}{3}

x = \frac{5 81 y + 324}{3}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph