Algebra Examples

$f (x) = \sqrt{x + 1}$ , $g (x) = x^{2} - 1$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x^{2} - 1)$ by substituting in the value of $g$ into $f$ .

$f (x^{2} - 1) = \sqrt{(x^{2} - 1) + 1}$

Step 3

Set the radicand in $\sqrt{(x^{2} - 1) + 1}$ greater than or equal to $0$ to find where the expression is defined.

$(x^{2} - 1) + 1 \geq 0$

Step 4

Solve for $x$ .

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Step 4.1

Combine the opposite terms in $x^{2} - 1 + 1$ .

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Step 4.1.1

Add $- 1$ and $1$ .

$x^{2} + 0 \geq 0$

Step 4.1.2

Add $x^{2}$ and $0$ .

$x^{2} \geq 0$

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