QuestionTentukan $f(g(x))$ untuk $f(x)=\frac{x-1}{x+1}, x \neq-1$ dan $g(x)=\frac{1}{x}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given as $\frac{x-1}{x+1}$ with $x \neq -1$ . The function $g(x)$ is given as $\frac{1}{x}$
3. We need to find the composition of the functions, denoted as $f(g(x))$

STEP 2

The composition of functions $f(g(x))$ means we substitute $g(x)$ into the function $f(x)$ .
$f(g(x)) = f\left(\frac{1}{x}\right)$

STEP 3

Now, substitute $\frac{1}{x}$ into $f(x)$ .
$f\left(\frac{1}{x}\right) = \frac{\frac{1}{x}-1}{\frac{1}{x}+1}$

STEP 4

To simplify this expression, we can multiply the numerator and denominator by $x$ to get rid of the fraction within a fraction.
$f\left(\frac{1}{x}\right) = \frac{x(\frac{1}{x}-1)}{x(\frac{1}{x}+1)}$

STEP 5

implify the expression.
$f\left(\frac{1}{x}\right) = \frac{1-x}{1+x}$ So, $f(g(x))$ in its simplest form is $\frac{1-x}{1+x}$ .

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