Find f(g(x)) f(x)=x/(x+1) , g(x)=11/x

$f (x) = \frac{x}{x + 1}$ , $g (x) = \frac{11}{x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{11}{x})$ by substituting in the value of $g$ into $f$ .

$f (\frac{11}{x}) = \frac{\frac{11}{x}}{(\frac{11}{x}) + 1}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{11}{x}) = \frac{11}{x} \cdot \frac{1}{\frac{11}{x} + 1}$

Step 4

Simplify the denominator.

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

$f (\frac{11}{x}) = \frac{11}{x} \cdot \frac{1}{\frac{11}{x} + \frac{x}{x}}$

Combine the numerators over the common denominator.

$f (\frac{11}{x}) = \frac{11}{x} \cdot \frac{1}{\frac{11 + x}{x}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{11}{x}) = \frac{11}{x} \cdot (1 (\frac{x}{11 + x}))$

Step 6

Multiply $\frac{x}{11 + x}$ by $1$ .

$f (\frac{11}{x}) = \frac{11}{x} \cdot \frac{x}{11 + x}$

Step 7

Cancel the common factor of $x$ .

Cancel the common factor.

$f (\frac{11}{x}) = \frac{11}{x} \cdot \frac{x}{11 + x}$

Rewrite the expression.

$f (\frac{11}{x}) = 11 (\frac{1}{11 + x})$

Step 8

Combine $11$ and $\frac{1}{11 + x}$ .

$f (\frac{11}{x}) = \frac{11}{11 + x}$