Calculus Examples

$g (x) = - 3^{4} + 30 x^{2} - 27$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Raise $3$ to the power of $4$ .

$g x = - 1 \cdot 81 + 30 x^{2} - 27$

Step 1.2

Multiply $- 1$ by $81$ .

$g x = - 81 + 30 x^{2} - 27$

Step 1.3

Subtract $27$ from $- 81$ .

$g x = 30 x^{2} - 108$

Step 2

Divide each term in $g x = 30 x^{2} - 108$ by $x$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $g x = 30 x^{2} - 108$ by $x$ .

$\frac{g x}{x} = \frac{30 x^{2}}{x} + \frac{- 108}{x}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{g x}{x} = \frac{30 x^{2}}{x} + \frac{- 108}{x}$

Step 2.2.1.2

Divide $g$ by $1$ .

$g = \frac{30 x^{2}}{x} + \frac{- 108}{x}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Simplify each term.

Tap for more steps...

Step 2.3.1.1

Cancel the common factor of $x^{2}$ and $x$ .

Tap for more steps...

Step 2.3.1.1.1

Factor $x$ out of $30 x^{2}$ .

$g = \frac{x (30 x)}{x} + \frac{- 108}{x}$

Step 2.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 2.3.1.1.2.1

Raise $x$ to the power of $1$ .

$g = \frac{x (30 x)}{x^{1}} + \frac{- 108}{x}$

Step 2.3.1.1.2.2

Factor $x$ out of $x^{1}$ .

$g = \frac{x (30 x)}{x \cdot 1} + \frac{- 108}{x}$

Step 2.3.1.1.2.3

Cancel the common factor.

$g = \frac{x (30 x)}{x \cdot 1} + \frac{- 108}{x}$

Step 2.3.1.1.2.4

Rewrite the expression.

$g = \frac{30 x}{1} + \frac{- 108}{x}$

Step 2.3.1.1.2.5

Divide $30 x$ by $1$ .

$g = 30 x + \frac{- 108}{x}$

Step 2.3.1.2

Move the negative in front of the fraction.

$g = 30 x - \frac{108}{x}$

Step 3

To rewrite as a function of $x$ , write the equation so that $g$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = 30 x - \frac{108}{x}$