Solve y=x^2 4x-2 - ScanMath

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = \frac{3 2 x + 4}{2}

Evaluate

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

Simplify

More Steps

Evaluate

x^{2} \times 4 x - 2

Multiply

More Steps

Evaluate

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

4 x^{3} - 2

y = 4 x^{3} - 2

Interchange x and y

x = 4 y^{3} - 2

Swap the sides of the equation

4 y^{3} - 2 = x

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

4 y^{3} = x + 2

Divide both sides

\frac{4 y ^{3}}{4} = \frac{x + 2}{4}

Divide the numbers

y^{3} = \frac{x + 2}{4}

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

3 y^{3} = 3 \frac{x + 2}{4}

Calculate

y = 3 \frac{x + 2}{4}

Simplify the root

More Steps

Evaluate

3 \frac{x + 2}{4}

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

\frac{3 x + 2}{3 4}

Multiply by the Conjugate

\frac{3 x + 2 \times 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Calculate

\frac{3 x + 2 \times 3 4 ^{2}}{2 ^{2}}

Calculate

More Steps

Evaluate

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

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

3 (x + 2) \times 4^{2}

Calculate the product

3 16 x + 32

Factor the expression

3 16 (x + 2)

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

316 \times 3 x + 2

Evaluate the root

232 \times 3 x + 2

Calculate the product

2 3 2 x + 4

\frac{2 3 2 x + 4}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 2 x + 4}{2}

y = \frac{3 2 x + 4}{2}

Solution

f^{- 1} (x) = \frac{3 2 x + 4}{2}

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^{2} 4 x - 2

Simplify the expression

y = 4 x^{3} - 2

To test if the graph of y = 4 x^{3} - 2 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = 4 (- x)^{3} - 2

Simplify

More Steps

Evaluate

4 (- x)^{3} - 2

Multiply the terms

More Steps

Evaluate

4 (- x)^{3}

Rewrite the expression

4 (- x^{3})

Multiply the numbers

- 4 x^{3}

- 4 x^{3} - 2

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

Change the signs both sides

y = 4 x^{3} + 2

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{3 2 y + 4}{2}

Evaluate

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

Simplify

More Steps

Evaluate

x^{2} \times 4 x - 2

Multiply

More Steps

Evaluate

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

4 x^{3} - 2

y = 4 x^{3} - 2

Swap the sides of the equation

4 x^{3} - 2 = y

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

4 x^{3} = y + 2

Divide both sides

\frac{4 x ^{3}}{4} = \frac{y + 2}{4}

Divide the numbers

x^{3} = \frac{y + 2}{4}

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

3 x^{3} = 3 \frac{y + 2}{4}

Calculate

x = 3 \frac{y + 2}{4}

Solution

More Steps

Evaluate

3 \frac{y + 2}{4}

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

\frac{3 y + 2}{3 4}

Multiply by the Conjugate

\frac{3 y + 2 \times 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Calculate

\frac{3 y + 2 \times 3 4 ^{2}}{2 ^{2}}

Calculate

More Steps

Evaluate

3 y + 2 \times 3 4^{2}

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

3 (y + 2) \times 4^{2}

Calculate the product

3 16 y + 32

Factor the expression

3 16 (y + 2)

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

316 \times 3 y + 2

Evaluate the root

232 \times 3 y + 2

Calculate the product

2 3 2 y + 4

\frac{2 3 2 y + 4}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 2 y + 4}{2}

x = \frac{3 2 y + 4}{2}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph