Write as a Function of x g(x)=10-x^2

$g (x) = 10 - x^{2}$

Step 1

Divide each term in $g x = 10 - x^{2}$ by $x$ and simplify.

Divide each term in $g x = 10 - x^{2}$ by $x$ .

$\frac{g x}{x} = \frac{10}{x} + \frac{- x^{2}}{x}$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{g x}{x} = \frac{10}{x} + \frac{- x^{2}}{x}$

Divide $g$ by $1$ .

$g = \frac{10}{x} + \frac{- x^{2}}{x}$

Simplify the right side.

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

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

$g = \frac{10}{x} + \frac{x (- x)}{x}$

Cancel the common factors.

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

$g = \frac{10}{x} + \frac{x (- x)}{x^{1}}$

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

$g = \frac{10}{x} + \frac{x (- x)}{x \cdot 1}$

Cancel the common factor.

$g = \frac{10}{x} + \frac{x (- x)}{x \cdot 1}$

Rewrite the expression.

$g = \frac{10}{x} + \frac{- x}{1}$

Divide $- x$ by $1$ .

$g = \frac{10}{x} - x$

Step 2

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.

$f (x) = \frac{10}{x} - x$

Write as a Function of x g(x)=10-x^2

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