Algebra Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x + 1)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Remove parentheses.

$\sqrt{x + 1}$

Step 4

Set the radicand in $\sqrt{x + 1}$ greater than or equal to $0$ to find where the expression is defined.

$x + 1 \geq 0$

Step 5

Subtract $1$ from both sides of the inequality.

$x \geq - 1$

Step 6

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

Interval Notation:

$[- 1, \infty)$

Set-Builder Notation:

${x | x \geq - 1}$

Step 7

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