Algebra Examples

$f (x) = x^{2} + 6$ , $g (x) = \sqrt{1 - x}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} + 6)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} + 6) = \sqrt{1 - (x^{2} + 6)}$

Step 3

Apply the distributive property.

$g (x^{2} + 6) = \sqrt{1 - x^{2} - 1 \cdot 6}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 1$ by $6$ .

$g (x^{2} + 6) = \sqrt{1 - x^{2} - 6}$

Step 4.2

Subtract $6$ from $1$ .

$g (x^{2} + 6) = \sqrt{- x^{2} - 5}$