Solve y=x^22x-4 - ScanMath

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = \frac{3 4 x + 16}{2}

Evaluate

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

Simplify

More Steps

Evaluate

x^{2} \times 2 x - 4

Multiply

More Steps

Evaluate

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

2 x^{3} - 4

y = 2 x^{3} - 4

Interchange x and y

x = 2 y^{3} - 4

Swap the sides of the equation

2 y^{3} - 4 = x

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

2 y^{3} = x + 4

Divide both sides

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

Divide the numbers

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

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

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

Calculate

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

Simplify the root

More Steps

Evaluate

3 \frac{x + 4}{2}

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

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

Multiply by the Conjugate

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

Calculate

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

Calculate

More Steps

Evaluate

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

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

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

Calculate the product

3 4 x + 16

\frac{3 4 x + 16}{2}

y = \frac{3 4 x + 16}{2}

Solution

f^{- 1} (x) = \frac{3 4 x + 16}{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} 2 x - 4

Simplify the expression

y = 2 x^{3} - 4

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

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

Simplify

More Steps

Evaluate

2 (- x)^{3} - 4

Multiply the terms

More Steps

Evaluate

2 (- x)^{3}

Rewrite the expression

2 (- x^{3})

Multiply the numbers

- 2 x^{3}

- 2 x^{3} - 4

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

Change the signs both sides

y = 2 x^{3} + 4

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{3 4 y + 16}{2}

Evaluate

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

Simplify

More Steps

Evaluate

x^{2} \times 2 x - 4

Multiply

More Steps

Evaluate

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

2 x^{3} - 4

y = 2 x^{3} - 4

Swap the sides of the equation

2 x^{3} - 4 = y

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

2 x^{3} = y + 4

Divide both sides

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

Divide the numbers

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

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

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

Calculate

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

Solution

More Steps

Evaluate

3 \frac{y + 4}{2}

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

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

Multiply by the Conjugate

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

Calculate

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

Calculate

More Steps

Evaluate

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

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

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

Calculate the product

3 4 y + 16

\frac{3 4 y + 16}{2}

x = \frac{3 4 y + 16}{2}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph