Find the Domain of the Composition f(g(x)) f(x)=3x+1 , g(x) = square root of x

$f (x) = 3 x + 1$ , $g (x) = \sqrt{x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (\sqrt{x}) = 3 (\sqrt{x}) + 1$

Step 3

Set the radicand in $\sqrt{x}$ greater than or equal to $0$ to find where the expression is defined.

$x \geq 0$

Step 4

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 5