Find f(g(x)) f(x)=-1/(6x) g(x)=1/(6x)

$f (x) = - \frac{1}{6 x}$ $g (x) = \frac{1}{6 x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{1}{6 x})$ by substituting in the value of $g$ into $f$ .

$f (\frac{1}{6 x}) = - \frac{1}{6 (\frac{1}{6 x})}$

Step 3

Combine $6$ and $\frac{1}{6 x}$ .

$f (\frac{1}{6 x}) = - \frac{1}{\frac{6}{6 x}}$

Step 4

Reduce the expression $\frac{6}{6 x}$ by cancelling the common factors.

Cancel the common factor.

$f (\frac{1}{6 x}) = - \frac{1}{\frac{6}{6 x}}$

Rewrite the expression.

$f (\frac{1}{6 x}) = - \frac{1}{\frac{1}{x}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{1}{6 x}) = - (1 x)$

Step 6

Multiply $x$ by $1$ .

$f (\frac{1}{6 x}) = - x$