Algebra Examples

$f (x) = \frac{1 - x}{9 x}$ , $g (x) = \frac{1}{1 + 9 x}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{1 - x}{9 x})$ by substituting in the value of $f$ into $g$ .

$g (\frac{1 - x}{9 x}) = \frac{1}{1 + 9 (\frac{1 - x}{9 x})}$

Step 3

Simplify the denominator.

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Step 3.1

Cancel the common factor of $9$ .

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Step 3.1.1

Factor $9$ out of $9 x$ .

$g (\frac{1 - x}{9 x}) = \frac{1}{1 + 9 (\frac{1 - x}{9 (x)})}$

Step 3.1.2

Cancel the common factor.

$g (\frac{1 - x}{9 x}) = \frac{1}{1 + 9 (\frac{1 - x}{9 x})}$

Step 3.1.3

Rewrite the expression.

$g (\frac{1 - x}{9 x}) = \frac{1}{1 + \frac{1 - x}{x}}$

Step 3.2

Write $1$ as a fraction with a common denominator.

$g (\frac{1 - x}{9 x}) = \frac{1}{\frac{x}{x} + \frac{1 - x}{x}}$

Step 3.3

Combine the numerators over the common denominator.

$g (\frac{1 - x}{9 x}) = \frac{1}{\frac{x + 1 - x}{x}}$

Step 3.4

Reorder terms.

$g (\frac{1 - x}{9 x}) = \frac{1}{\frac{x - x + 1}{x}}$

Step 3.5

Rewrite $\frac{x - x + 1}{x}$ in a factored form.

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Step 3.5.1

Subtract $x$ from $x$ .

$g (\frac{1 - x}{9 x}) = \frac{1}{\frac{0 + 1}{x}}$

Step 3.5.2

Add $0$ and $1$ .

$g (\frac{1 - x}{9 x}) = \frac{1}{\frac{1}{x}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{1 - x}{9 x}) = 1 x$

Step 5

Multiply $x$ by $1$ .

$g (\frac{1 - x}{9 x}) = x$