Algebra Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

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

Tap for more steps...

Step 3.3.1

Add $- x$ and $x$ .

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

Step 3.3.2

Add $1$ and $0$ .

$f (\frac{1 - x}{x}) = \frac{1}{\frac{1}{x}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{1 - x}{x}) = 1 x$

Step 5

Multiply $x$ by $1$ .

$f (\frac{1 - x}{x}) = x$