Algebra Examples

$f (x) = \sqrt{x + 4}$ , $g (x) = x^{2}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x^{2})$ by substituting in the value of $g$ into $f$ .

$f (x^{2}) = \sqrt{(x^{2}) + 4}$

Step 3

Set the radicand in $\sqrt{(x^{2}) + 4}$ greater than or equal to $0$ to find where the expression is defined.

$(x^{2}) + 4 \geq 0$

Step 4

Solve for $x$ .

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Step 4.1

Subtract $4$ from both sides of the inequality.

$x^{2} \geq - 4$

Step 4.2

Since the left side has an even power, it is always positive for all real numbers.

All real numbers

Step 5

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 6