Algebra Examples

$h (x) = \sqrt{x + 3}$ and $k (x) = 2 x + 7$

Step 1

Set up the composite result function.

$h (k (x))$

Step 2

Evaluate $h (2 x + 7)$ by substituting in the value of $k$ into $h$ .

$h (2 x + 7) = \sqrt{(2 x + 7) + 3}$

Step 3

Add $7$ and $3$ .

$h (2 x + 7) = \sqrt{2 x + 10}$

Step 4

Factor $2$ out of $2 x + 10$ .

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Step 4.1

Factor $2$ out of $2 x$ .

$h (2 x + 7) = \sqrt{2 (x) + 10}$

Step 4.2

Factor $2$ out of $10$ .

$h (2 x + 7) = \sqrt{2 x + 2 \cdot 5}$

Step 4.3

Factor $2$ out of $2 x + 2 \cdot 5$ .

$h (2 x + 7) = \sqrt{2 (x + 5)}$