Algebra Examples

$f (x) = x^{2}$ , $g (x) = x - 1$

Distribute the value across the operation.

$f (x) \div g x$

Evaluate $f (x)$ .

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Replace the variable $x$ with $x$ in the expression.

$f (x) = {(x)}^{2}$

Simplify the result.

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Remove parentheses around $x$ .

$f (x) = x^{2}$

The final answer is $x^{2}$ .

$x^{2}$

Evaluate $g (x)$ .

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Replace the variable $x$ with $x$ in the expression.

$g (x) = (x) - 1$

Simplify the result.

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Remove parentheses around $x$ .

$g (x) = x - 1$

The final answer is $x - 1$ .

$x - 1$

Compose the result function for $f (x) \div g x$ by replacing the function designators with the actual functions.

$x^{2} \div (x - 1)$

Rewrite the division as a fraction.

$\frac{x^{2}}{x - 1}$

Solve to find the value of $x$ that makes the expression undefined.

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Set up the equation to solve for $x$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

For asymptotes and point discontinuity (denominator equals $0$ ), it is easier to find where the expression is undefined. These values are not part of the domain.

$x - 1 = 0$

The domain is all values of $x$ that make the expression defined.

$(- \infty, 1) \cup (1, \infty)$

${x | x \neq 1}$

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