Solve y=5x^2 8x-6

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (x) = \frac{3 25 x + 150}{10}

Evaluate

y = 5 x^{2} \times 8 x - 6

Simplify

More Steps

Evaluate

5 x^{2} \times 8 x - 6

Multiply

More Steps

Evaluate

5 x^{2} \times 8 x

Multiply the terms

40 x^{2} \times x

Multiply the terms with the same base by adding their exponents

40 x^{2 + 1}

Add the numbers

40 x^{3}

40 x^{3} - 6

y = 40 x^{3} - 6

Interchange x and y

x = 40 y^{3} - 6

Swap the sides of the equation

40 y^{3} - 6 = x

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

40 y^{3} = x + 6

Divide both sides

\frac{40 y ^{3}}{40} = \frac{x + 6}{40}

Divide the numbers

y^{3} = \frac{x + 6}{40}

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

3 y^{3} = 3 \frac{x + 6}{40}

Calculate

y = 3 \frac{x + 6}{40}

Simplify the root

More Steps

Evaluate

3 \frac{x + 6}{40}

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

\frac{3 x + 6}{3 40}

Simplify the radical expression

More Steps

Evaluate

340

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 5

Write the number in exponential form with the base of 2

3 2^{3} \times 5

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

3 2^{3} \times 35

Reduce the index of the radical and exponent with 3

235

\frac{3 x + 6}{2 3 5}

Multiply by the Conjugate

\frac{3 x + 6 \times 3 5 ^{2}}{2 3 5 \times 3 5 ^{2}}

Calculate

\frac{3 x + 6 \times 3 5 ^{2}}{2 \times 5}

Calculate

More Steps

Evaluate

3 x + 6 \times 3 5^{2}

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

3 (x + 6) \times 5^{2}

Calculate the product

3 25 x + 150

\frac{3 25 x + 150}{2 \times 5}

Calculate

\frac{3 25 x + 150}{10}

y = \frac{3 25 x + 150}{10}

Solution

f^{- 1} (x) = \frac{3 25 x + 150}{10}

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 x^{2} 8 x - 6

Simplify the expression

y = 40 x^{3} - 6

To test if the graph of y = 40 x^{3} - 6 is symmetry with respect to the origin,substitute -x for x and -y for y

- y = 40 (- x)^{3} - 6

Simplify

More Steps

Evaluate

40 (- x)^{3} - 6

Multiply the terms

More Steps

Evaluate

40 (- x)^{3}

Rewrite the expression

40 (- x^{3})

Multiply the numbers

- 40 x^{3}

- 40 x^{3} - 6

- y = - 40 x^{3} - 6

Change the signs both sides

y = 40 x^{3} + 6

Solution

Not symmetry with respect to the origin

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{3 25 y + 150}{10}

Evaluate

y = 5 x^{2} \times 8 x - 6

Simplify

More Steps

Evaluate

5 x^{2} \times 8 x - 6

Multiply

More Steps

Evaluate

5 x^{2} \times 8 x

Multiply the terms

40 x^{2} \times x

Multiply the terms with the same base by adding their exponents

40 x^{2 + 1}

Add the numbers

40 x^{3}

40 x^{3} - 6

y = 40 x^{3} - 6

Swap the sides of the equation

40 x^{3} - 6 = y

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

40 x^{3} = y + 6

Divide both sides

\frac{40 x ^{3}}{40} = \frac{y + 6}{40}

Divide the numbers

x^{3} = \frac{y + 6}{40}

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

3 x^{3} = 3 \frac{y + 6}{40}

Calculate

x = 3 \frac{y + 6}{40}

Solution

More Steps

Evaluate

3 \frac{y + 6}{40}

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

\frac{3 y + 6}{3 40}

Simplify the radical expression

More Steps

Evaluate

340

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 5

Write the number in exponential form with the base of 2

3 2^{3} \times 5

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

3 2^{3} \times 35

Reduce the index of the radical and exponent with 3

235

\frac{3 y + 6}{2 3 5}

Multiply by the Conjugate

\frac{3 y + 6 \times 3 5 ^{2}}{2 3 5 \times 3 5 ^{2}}

Calculate

\frac{3 y + 6 \times 3 5 ^{2}}{2 \times 5}

Calculate

More Steps

Evaluate

3 y + 6 \times 3 5^{2}

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

3 (y + 6) \times 5^{2}

Calculate the product

3 25 y + 150

\frac{3 25 y + 150}{2 \times 5}

Calculate

\frac{3 25 y + 150}{10}

x = \frac{3 25 y + 150}{10}

Show Solution

Function

Testing for symmetry

Solve the equation

Graph