Find the Domain f(x)=1/x , g(x)=x^2 , g(f(x))

$f (x) = \frac{1}{x}$ , $g (x) = x^{2}$ , $g (f (x))$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (\frac{1}{x}) = {(\frac{1}{x})}^{2}$

Step 3

Set the denominator in $\frac{1}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 4

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0}$

Step 5