Solve m = a^2 3a 1

Question

Function

Find the inverse

Evaluate the derivative

Find the domain

f^{- 1} (a) = \frac{3 9 a}{3}

Evaluate

m = a^{2} \times 3 a \times 1

Simplify

More Steps

Evaluate

a^{2} \times 3 a \times 1

Rewrite the expression

a^{2} \times 3 a

Multiply the terms with the same base by adding their exponents

a^{2 + 1} \times 3

Add the numbers

a^{3} \times 3

Use the commutative property to reorder the terms

3 a^{3}

m = 3 a^{3}

Interchange a and y

a = 3 y^{3}

Swap the sides of the equation

3 y^{3} = a

Divide both sides

\frac{3 y ^{3}}{3} = \frac{a}{3}

Divide the numbers

y^{3} = \frac{a}{3}

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

3 y^{3} = 3 \frac{a}{3}

Calculate

y = 3 \frac{a}{3}

Simplify the root

More Steps

Evaluate

3 \frac{a}{3}

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

\frac{3 a}{3 3}

Multiply by the Conjugate

\frac{3 a \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Calculate

\frac{3 a \times 3 3 ^{2}}{3}

Calculate

More Steps

Evaluate

3 a \times 3 3^{2}

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

3 a \times 3^{2}

Calculate the product

3 3^{2} a

\frac{3 3 ^{2} a}{3}

Calculate

\frac{3 9 a}{3}

y = \frac{3 9 a}{3}

Solution

f^{- 1} (a) = \frac{3 9 a}{3}

Show Solution

Solve the equation

Solve for a

Solve for m

a = \frac{3 9 m}{3}

Evaluate

m = a^{2} \times 3 a \times 1

Simplify

More Steps

Evaluate

a^{2} \times 3 a \times 1

Rewrite the expression

a^{2} \times 3 a

Multiply the terms with the same base by adding their exponents

a^{2 + 1} \times 3

Add the numbers

a^{3} \times 3

Use the commutative property to reorder the terms

3 a^{3}

m = 3 a^{3}

Swap the sides of the equation

3 a^{3} = m

Divide both sides

\frac{3 a ^{3}}{3} = \frac{m}{3}

Divide the numbers

a^{3} = \frac{m}{3}

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

3 a^{3} = 3 \frac{m}{3}

Calculate

a = 3 \frac{m}{3}

Solution

More Steps

Evaluate

3 \frac{m}{3}

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

\frac{3 m}{3 3}

Multiply by the Conjugate

\frac{3 m \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Calculate

\frac{3 m \times 3 3 ^{2}}{3}

Calculate

More Steps

Evaluate

3 m \times 3 3^{2}

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

3 m \times 3^{2}

Calculate the product

3 3^{2} m

\frac{3 3 ^{2} m}{3}

Calculate

\frac{3 9 m}{3}

a = \frac{3 9 m}{3}

Show Solution

Function

Solve the equation

Graph